Intro. To Graphing Linear Equations

Size: px
Start display at page:

Download "Intro. To Graphing Linear Equations"

Transcription

1 Intro. To Graphing Linear Equations The Coordinate Plane A. The coordinate plane has 4 quadrants. B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate). The point is stated as an ordered pair (x,y). C. Horizontal Axis is the X Axis. (y = 0) D. Vertical Axis is the Y- Axis (x = 0) Plot the following points: a) (3,7) b) (-4,5) c) (-6,-1) d) (6,-7) e) (5,0) f) (0,5) g) (-5,0) f) (0, -5) y-axis x-axis 1

2 Slope Intercept Form Before graphing linear equations, we need to be familiar with slope intercept form. To understand slope intercept form, we need to understand two major terms: The slope and the y-intercept. Slope (m): The slope measures the steepness of a non-vertical line. It is sometimes referred to as the rise over run. It s how fast and in what direction y changes compared to x. y-intercept: The y-intercept is where a line passes through the y axis. It is always stated as an ordered pair (x,y). The x coordinate is always zero. The y coordinate can be found by plugging in 0 for the X in the equation or by finding exactly where the line crosses the y-axis. What are the coordinates of the y-intercept line pictured in the diagram above? : Some of you have worked with slope intercept form of a linear equation before. You may remember: y = mx + b Using y = mx + b, can you figure out the equation of the line pictured above?: 2

3 Graphing Linear Equations Graphing The Linear Equation: y = 3x - 5 1) Find the slope: m = 3 m = 3. = y. 1 x 2) Find the y-intercept: x = 0, b = -5 (0, -5) 3) Plot the y-intercept 4) Use slope to find the next point: Start at (0,-5) m = 3. = y. up 3 on the y-axis 1 x right 1 on the x-axis (1,-2) Repeat: (2,1) (3,4) (4,7) 5) To plot to the left side of the y-axis, go to y-int. and do the opposite. (Down 3 on the y, left 1 on the x) (-1,-8) 6) Connect the dots. Do Now: 1) y = 2x + 1 2) y = -4x + 5 3

4 3) y = ½ x 3 4) y= - ⅔x + 2 5) y = -x 3 6) y= 5x 4

5 Q3 Quiz 1 Review Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 1) y = 4x - 6 2) y = -2x + 7 5

6 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 3) y = -x - 5 4) y = 5x + 5 6

7 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 5) y = - ½ x - 7 6) y = ⅗x - 4 7

8 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 7) y = ⅔x 8) y = - ⅓x + 4 8

9 Finding the equation of a line in slope intercept form (y=mx + b) Example: Using slope intercept form [y = mx + b] Find the equation in slope intercept form of the line formed by (1,2) and (-2, -7). A. Find the slope (m): B. Use m and one point to find b: m = y 2 y 1 y = mx + b x 2 x 1 m= 3 x= 1 y= 2 m = (-7) (2). 2 = 3(1) + b (-2) (1) 2 = 3 + b -3-3 m = = b -3 m= 3 y = 3x 1 Example: Using point slope form [ y y 1 = m(x x 1 ) ] Find the equation in slope intercept form of the line formed by (1,2) and (-2, -7). A. Find the slope (m): B. Use m and one point to find b: m = y 2 y 1 y y 1 = m(x x 1 ) x 2 x 1 m= 3 x= 1 y= 2 y (2) = 3(x (1)) m = (-7) (2). y 2 = 3x - 3 (-2) (1) m = -9. y = 3x 1-3 m= 3 9

10 Find the equation in slope intercept form of the line formed by the given points. When you re finished, graph the equation on the give graph. 1) (4,-6) and (-8, 3) 10

11 2) (4,-3) and (9,-3) 3) (7,-2) and (7, 4) III. Special Slopes A. Zero Slope B. No Slope (undefined slope) * No change in Y * No change in X * Equation will be Y = * Equation will be X = * Horizontal Line * Vertical Line 11

12 Point-Slope Form y y 1 = m(x x 1 ) Slope Intercept Form y = mx + b y is by itself Standard Form: Ax + By = C Constant (number) is by itself Given the slope and 1 point, write the equation of the line in: (a) point-slope form, (b) slope intercept form, and (c) standard form: Example: m = ½ ; (-6,-1) a) Point-Slope Form b) Slope intercept form c) Standard Form 1) m = -2; (-3,1) a) Point-Slope Form b) Slope intercept form c) Standard Form 12

13 2) m = - ¾ ; (-8, 5) Point-Slope Form b) Slope intercept form c) Standard Form 3) m = ⅔; (-6, -4) Point-Slope Form b) Slope intercept form c) Standard Form 4) m = -1 (5, -1) Point-Slope Form b) Slope intercept form c) Standard Form 13

14 Find equation in slope intercept form and graph: 1) (3,-2)(-6,-8) 2) (-6,10) (9,-10) 3) (3,7) (3,-7) 4) (7,-6)(-3,4) 14

15 5) (5,-9)(-5,-9) 6) m= 4 (-2,-5) 7) m= ⅔ (-6,-7) 8) m= - (8,-1) 15

16 9) m = 0 (4,3) 10) m = undefined (-6, 5) 11) 16x -4y =36 12) 8x+24y = 96 16

17 13) y+7=2(x+1) 14) y+5=(2/5)(x+10) 15) y-7= ¾ (x-12) 16) y-2=-3(x-2) 17

18 Q3 Quiz 2 Review Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 1) y - 2 = -3(x 1) 2) 14x + 21y =

19 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 3) y + 10 = 5(x + 2) 4) y 7 = ¼ (x 20) 19

20 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 5) 8x 8y = 56 6) y + 6 = -1(x 4) 20

21 Find the equation in slope intercept form and graph: If your printer doesn t print the graphs, you must use your own graph paper. 7) 18x 12y = -12 8) y 15 = (-5/3)(x + 9) Answers: 1) y = -3x + 5 2) y = - ⅔ x - 4 3) y = 5x 4) y = ¼ x + 2 5) y = x - 7 6) y = - x 3 7) y = (3/2)x - 1 8) y = -(5/3)x 21

22 Graph both of the lines on the same set of axis: y = -2x + 6 y = -2x 5 IV. Parallel and Perpendicular Lines: A. Parallel Lines * Do not intersect * Have same slopes For the given line, find a line that is parallel and passes through the given point and graph Given Line: Parallel: Given Line: Parallel: 7) y = ⅓ x + 4 (6,1) 8) y = 4x 5 (2,13) Given Line: Parallel: Given Line: Parallel: 9) y = -⅔ x + 2 (-9,2) 10) y = 5x + 6 (4,-27) 22

23 Practice Problems: a) Use the two points to find the equation of the line. b) For the line found in part a, find a line that is parallel and passes through the given point. c) Graph both lines on the same set of axis. Given Line: Parallel: 1) (-5, 13) (3, -3) (4,-10) Given Line: Parallel: 2) (-6,0) (3,6) (6,3) 23

24 Given Line: Parallel: 3) (2,6)(-3,-19) (5,30) Given Line: Parallel: 4) (-4,3) (-8,6) (-4, 10) 24

25 Given Line: Parallel: 5) (2,-5) (-2, -5) (8,-2) Given Line: Parallel: 6) (-9,-11)(6,9) (-3,-9) 25

26 Given Line: Parallel: 7) (8,-3) (-4,9) (-2, 1) Given Line: Parallel: 8) (3,6)(3,-6) (7,-3) 26

27 Given Line: Parallel: 9) (4,-3)(-6,-8) (6,7) Given Line: Parallel: 10) (2,4)(-6,-12) (-3,-5) 27

28 11) Find the equation of the line parallel to y = 3x 2, passing through (-2, 1). 12) Find the equation of the line parallel to y = -½x 5, passing through (-2, 7) 13) Find the equation of the line parallel to y = -¼ x + 2, passing through (-8, 4) 14) Find the equation of the line parallel to y = (3/2)x + 6, passing through (-6, -11) 15) Find the equation of the line parallel to y = -5, passing through (2,7) 16) Find the equation of the line parallel to x = 5, passing through (6, -4). 28

29 Q3 Quiz 3 Review FOLLOW REQUIRED FORMAT AND SHOW ALL PROPER WORK! a) Use the two points to find the equation of the line. b) For the line found in part a, find a line that is parallel and passes through the given point. c) Graph both lines on the same set of axis. Given Line: Parallel: 1) (-4, 13) (3, -8) (4,-17) Given Line: Parallel: 2) (8,1) (-4,-5) (-6,2) 29

30 Given Line: Parallel: 3) (5,4) (-4,4) (-6,-7) For # s 4-7, just find the equation. You do not have to graph. 4) Find the equation of the line parallel to y = -⅗x 2, passing through (-5, 7). 5) Find the equation of the line parallel to y = 4x 5, passing through (-4, 9) 6) Find the equation of the line parallel to y = 2, passing through (-8, -9) 7) Find the equation of the line parallel to x = 5, passing through (-6, -11) 30

31 Solving Systems of Equations Graphically A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. When solving a system containing two linear equations there will be one ordered pair (x,y) that will work in both equations. To solve such a system graphically, we will graph both lines on the same set of axis and look for the point of intersection. The point of intersection will be the one ordered pair that works in both equations. We must then CHECK the solution by substituting the x and y coordinates in BOTH ORIGINAL EQUATIONS. 1) Solve the following system graphically: y = 2x 5 y = - ⅓x

32 Solve each of the systems of equations graphically: 2) y + 1 = -3(x 1) 7x + 7y = 42 3) y 9 = ¾ (x 12) 6x + 12y =

33 4) 12x 8y = 48 y 4 = -2(x 2) 5) y + 5 = 2(x + 4) y 10 = - ½ (x + 4) 33

34 Solve each system graphically and check: 6) y = -4x -5 y = 2x -7 7) 6x + 3y =21 12x + 16y =

35 8) 12x 6y = -6 16x -8y = 40 9) y= -4 x = 7 35

36 10) y-2= (3/5)(x-10) y+11 =2(x+7) 11) 6x + 9y = 45 9x +15y = 75 36

37 12) x = 5 y-12 = -3(x+2) 13) 9x 18y = 126 y = -4 37

38 Q3 Quiz 4 Review 1) y = 2x + 6 y = - ½x - 4 2) 15x - 15y = -45 y - 2 = -3(x + 1) 38

39 3) y + 3 = (-2/3)(x - 3) y + 1 = -1(x + 2) 4) 24x - 18y = -18 y = -7 39

40 5) y + 2 = (-3/4)(x - 8) 17x - 34y = 204 6) x = -6 y + 15 = (5/3)(x + 9) 40

41 7) y - 5 = ¼(x - 4) 45x - 15y = 105 8) 24x - 12y = -72 y 2 = 2(x + 2) 41

42 9) 11x + 44y = -176 y - 3 = - ¼ (x + 4) 10) y + 4 = (2/3)(x + 12) 25x + 50y = -150 Answer Key: 1) (-4,-2) 2) (-1,2) 3) (-6,3) 4) (-6, -7) 5) (8,-2) 6) (-6,-10) 7) (4,5) 8) Many Solutions 9) No Solution 10) (-6,0) 42

43 Graphing Inequalities When we solved and graphed inequalities with only one variable (ex: x > 3), we moved on to compound inequalities (AND/OR). We would graph both inequalities on the same number line and decide what to keep based on whether it was an AND or an OR problem. When we graphed linear equations on the coordinate plane we moved on to solving systems of equations graphically. When we graph inequalities in two variables on the coordinate plane, we do not graph compound inequalities. We move on to solving systems of inequalities. It takes a little from both inequalities with one variable and solving systems graphically. Graph the Inequality: y > ¼ x + 3 Step 1: Graph the line. y > ¼ x + 3 m = ¼ = y = up 1 x r 4 y-int= (0,3) Step 2: Test a point one up from the from the y-int and one down from the y-int): (0, 2) (0, 4) 2 > ¼ (0)+3 4 > ¼ (0) > 3 4 > 3 FALSE TRUE Step 3: Shade towards the true point (0,4) When you test, you must do it in the original inequality! 43

44 1) 6x - 9y > 36 2) y - 3 > -2(x + 1) 44

45 3) 12x + 9y < 27 4) y + 4 > -3(x - 3) 45

46 5) y > 4 6) x < -6 46

47 Q3 Quiz 5 Review 1) 72x 216y < ) y + 1 > ⅖ (x + 10) 47

48 3) y 5 < - ½ (x + 10) 4) 48x + 12y <

49 5) x > 7 6) y < -2 49

50 7) x < -4 8) y > 6 50

51 Graphing Systems of Inequalities Solve the system of inequalities graphically: y > ¼ x + 3 y < 3x 5 Step 1: Graph the 1 st inequality Step 2: Graph the 2 nd inequality y > ¼ x + 3 y < 3x 5 m = ¼ = m = 3/1 = y-int= (0,3) y-int.= (0,-5) (0, 2) TEST (0, 4) (0-6) TEST (0,-4) 2 > ¼ (0)+3-3 > ¼ (0) < 3(0) < 3(0) > 3 4 > 3-6 < -5-4 < -5 FALSE TRUE TRUE FALSE Step 3: Label the area where the shading intersects with an S 51

52 2) y - 3 < - ⅓(x 6) 12x 6y > -12 3) x > 4 y < -5 52

53 4) 24x + 6x > -6 y > 2 5) y 6 < ⅔(x - 9) x < -3 53

54 Q3 Quiz 6 Review 1) y > 5 3x - y > -3 2) y + 6 > -½ (x - 8) y - 4 > 2(x 2) 54

55 3) 15x 45y < 90 x > 3 4) 21x 7y > 14 y- 3 > -¼ (x + 12) 55

Math 1313 Prerequisites/Test 1 Review

Math 1313 Prerequisites/Test 1 Review Math 1313 Prerequisites/Test 1 Review Test 1 (Prerequisite Test) is the only exam that can be done from ANYWHERE online. Two attempts. See Online Assignments in your CASA account. Note the deadline too.

More information

Graphing Linear Equations

Graphing Linear Equations Graphing Linear Equations A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. What am I learning today? How to graph a linear

More information

graphing_9.1.notebook March 15, 2019

graphing_9.1.notebook March 15, 2019 1 2 3 Writing the equation of a line in slope intercept form. In order to write an equation in y = mx + b form you will need the slope "m" and the y intercept "b". We will subsitute the values for m and

More information

Algebra Unit 2: Linear Functions Notes. Slope Notes. 4 Types of Slope. Slope from a Formula

Algebra Unit 2: Linear Functions Notes. Slope Notes. 4 Types of Slope. Slope from a Formula Undefined Slope Notes Types of Slope Zero Slope Slope can be described in several ways: Steepness of a line Rate of change rate of increase or decrease Rise Run Change (difference) in y over change (difference)

More information

Sec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle.

Sec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle. Algebra I Chapter 4 Notes Name Sec 4.1 Coordinates and Scatter Plots Coordinate Plane: Formed by two real number lines that intersect at a right angle. X-axis: The horizontal axis Y-axis: The vertical

More information

UNIT 4 NOTES. 4-1 and 4-2 Coordinate Plane

UNIT 4 NOTES. 4-1 and 4-2 Coordinate Plane UNIT 4 NOTES 4-1 and 4-2 Coordinate Plane y Ordered pairs on a graph have several names. (X coordinate, Y coordinate) (Domain, Range) (Input,Output) Plot these points and label them: a. (3,-4) b. (-5,2)

More information

Vertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once

Vertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once Algebra 2 Chapter 2 Domain input values, X (x, y) Range output values, Y (x, y) Function For each input, there is exactly one output Example: Vertical Line Test a relationship is a function, if NO vertical

More information

SNAP Centre Workshop. Graphing Lines

SNAP Centre Workshop. Graphing Lines SNAP Centre Workshop Graphing Lines 45 Graphing a Line Using Test Values A simple way to linear equation involves finding test values, plotting the points on a coordinate plane, and connecting the points.

More information

Review for Mastery Using Graphs and Tables to Solve Linear Systems

Review for Mastery Using Graphs and Tables to Solve Linear Systems 3-1 Using Graphs and Tables to Solve Linear Systems A linear system of equations is a set of two or more linear equations. To solve a linear system, find all the ordered pairs (x, y) that make both equations

More information

Section Graphs and Lines

Section Graphs and Lines Section 1.1 - Graphs and Lines The first chapter of this text is a review of College Algebra skills that you will need as you move through the course. This is a review, so you should have some familiarity

More information

Chapter 1. Linear Equations and Straight Lines. 2 of 71. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 1. Linear Equations and Straight Lines. 2 of 71. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter 1 Linear Equations and Straight Lines 2 of 71 Outline 1.1 Coordinate Systems and Graphs 1.4 The Slope of a Straight Line 1.3 The Intersection Point of a Pair of Lines 1.2 Linear Inequalities 1.5

More information

Forms of Linear Equations

Forms of Linear Equations 6. 1-6.3 Forms of Linear Equations Name Sec 6.1 Writing Linear Equations in Slope-Intercept Form *Recall that slope intercept form looks like y = mx + b, where m = slope and b = y=intercept 1) Writing

More information

Example 1: Give the coordinates of the points on the graph.

Example 1: Give the coordinates of the points on the graph. Ordered Pairs Often, to get an idea of the behavior of an equation, we will make a picture that represents the solutions to the equation. A graph gives us that picture. The rectangular coordinate plane,

More information

3-6 Lines in the Coordinate Plane

3-6 Lines in the Coordinate Plane 3-6 Lines in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and

More information

Math-2. Lesson 3-1. Equations of Lines

Math-2. Lesson 3-1. Equations of Lines Math-2 Lesson 3-1 Equations of Lines How can an equation make a line? y = x + 1 x -4-3 -2-1 0 1 2 3 Fill in the rest of the table rule x + 1 f(x) -4 + 1-3 -3 + 1-2 -2 + 1-1 -1 + 1 0 0 + 1 1 1 + 1 2 2 +

More information

3.5 Day 1 Warm Up. Graph each line. 3.4 Proofs with Perpendicular Lines

3.5 Day 1 Warm Up. Graph each line. 3.4 Proofs with Perpendicular Lines 3.5 Day 1 Warm Up Graph each line. 1. y = 4x 2. y = 3x + 2 3. y = x 3 4. y = 4 x + 3 3 November 2, 2015 3.4 Proofs with Perpendicular Lines Geometry 3.5 Equations of Parallel and Perpendicular Lines Day

More information

Graphing Linear Equations

Graphing Linear Equations Graphing Linear Equations Question 1: What is a rectangular coordinate system? Answer 1: The rectangular coordinate system is used to graph points and equations. To create the rectangular coordinate system,

More information

CHAPTER. Graphs of Linear Equations. 3.1 Introduction to Graphing 3.2 Graphing Linear Equations 3.3 More with Graphing 3.4 Slope and Applications

CHAPTER. Graphs of Linear Equations. 3.1 Introduction to Graphing 3.2 Graphing Linear Equations 3.3 More with Graphing 3.4 Slope and Applications Graphs of Linear Equations CHAPTER 3 3.1 Introduction to Graphing 3.2 Graphing Linear Equations 3.3 More with Graphing 3.4 Slope and Applications Slide 2 3.1 Introduction to Graphing OBJECTIVES a Plot

More information

slope rise run Definition of Slope

slope rise run Definition of Slope The Slope of a Line Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the

More information

Section 18-1: Graphical Representation of Linear Equations and Functions

Section 18-1: Graphical Representation of Linear Equations and Functions Section 18-1: Graphical Representation of Linear Equations and Functions Prepare a table of solutions and locate the solutions on a coordinate system: f(x) = 2x 5 Learning Outcome 2 Write x + 3 = 5 as

More information

FLC Ch 3. Ex 1 Plot the points Ex 2 Give the coordinates of each point shown. Sec 3.2: Solutions and Graphs of Linear Equations

FLC Ch 3. Ex 1 Plot the points Ex 2 Give the coordinates of each point shown. Sec 3.2: Solutions and Graphs of Linear Equations Math 100 Elementary Algebra Sec 3.1: The Rectangular Coordinate System x-axis and y-axis origin ordered pair x-coordinate y-coordinate quadrants (I, II, III, and IV) Rectangular/Cartesian Coordinate System

More information

GRAPHING WORKSHOP. A graph of an equation is an illustration of a set of points whose coordinates satisfy the equation.

GRAPHING WORKSHOP. A graph of an equation is an illustration of a set of points whose coordinates satisfy the equation. GRAPHING WORKSHOP A graph of an equation is an illustration of a set of points whose coordinates satisfy the equation. The figure below shows a straight line drawn through the three points (2, 3), (-3,-2),

More information

Writing and Graphing Linear Equations. Linear equations can be used to represent relationships.

Writing and Graphing Linear Equations. Linear equations can be used to represent relationships. Writing and Graphing Linear Equations Linear equations can be used to represent relationships. Linear equation An equation whose solutions form a straight line on a coordinate plane. Collinear Points that

More information

State the domain and range of the relation. EX: {(-1,1), (1,5), (0,3)} 1 P a g e Province Mathematics Southwest TN Community College

State the domain and range of the relation. EX: {(-1,1), (1,5), (0,3)} 1 P a g e Province Mathematics Southwest TN Community College A relation is a set of ordered pairs of real numbers. The domain, D, of a relation is the set of all first coordinates of the ordered pairs in the relation (the xs). The range, R, of a relation is the

More information

You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1

You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1 Name GRAPHICAL REPRESENTATION OF DATA: You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1 ) and (x, y ) is x1 x y1 y,.

More information

7.3 3-D Notes Honors Precalculus Date: Adapted from 11.1 & 11.4

7.3 3-D Notes Honors Precalculus Date: Adapted from 11.1 & 11.4 73 3-D Notes Honors Precalculus Date: Adapted from 111 & 114 The Three-Variable Coordinate System I Cartesian Plane The familiar xy-coordinate system is used to represent pairs of numbers (ordered pairs

More information

Algebra I Notes Linear Equations and Inequalities in Two Variables Unit 04c

Algebra I Notes Linear Equations and Inequalities in Two Variables Unit 04c Big Idea: Describe the similarities and differences between equations and inequalities including solutions and graphs. Skill: graph linear equations and find possible solutions to those equations using

More information

Section 7D Systems of Linear Equations

Section 7D Systems of Linear Equations Section 7D Systems of Linear Equations Companies often look at more than one equation of a line when analyzing how their business is doing. For example a company might look at a cost equation and a profit

More information

ax + by = 0. x = c. y = d.

ax + by = 0. x = c. y = d. Review of Lines: Section.: Linear Inequalities in Two Variables The equation of a line is given by: ax + by = c. for some given numbers a, b and c. For example x + y = 6 gives the equation of a line. A

More information

The Rectangular Coordinate System and Equations of Lines. College Algebra

The Rectangular Coordinate System and Equations of Lines. College Algebra The Rectangular Coordinate System and Equations of Lines College Algebra Cartesian Coordinate System A grid system based on a two-dimensional plane with perpendicular axes: horizontal axis is the x-axis

More information

NOTES Linear Equations

NOTES Linear Equations NOTES Linear Equations Linear Parent Function Linear Parent Function the equation that all other linear equations are based upon (y = x) Horizontal and Vertical Lines (HOYY VUXX) V vertical line H horizontal

More information

3, 10,( 2, 4) Name. CP Algebra II Midterm Review Packet Unit 1: Linear Equations and Inequalities. Solve each equation. 3.

3, 10,( 2, 4) Name. CP Algebra II Midterm Review Packet Unit 1: Linear Equations and Inequalities. Solve each equation. 3. Name CP Algebra II Midterm Review Packet 018-019 Unit 1: Linear Equations and Inequalities Solve each equation. 1. x. x 4( x 5) 6x. 8x 5(x 1) 5 4. ( k ) k 4 5. x 4 x 6 6. V lhw for h 7. x y b for x z Find

More information

Did You Find a Parking Space?

Did You Find a Parking Space? Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the

More information

Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics

Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics 1 DISTANCE BETWEEN TWO POINTS - REVIEW To find the distance between two points, use the Pythagorean theorem. The difference between x 1 and x

More information

Algebra 1 Semester 2 Final Review

Algebra 1 Semester 2 Final Review Team Awesome 011 Name: Date: Period: Algebra 1 Semester Final Review 1. Given y mx b what does m represent? What does b represent?. What axis is generally used for x?. What axis is generally used for y?

More information

Chapter 4: Solving Linear Equations Study Guide

Chapter 4: Solving Linear Equations Study Guide 4.1: Plot Points in the Coordinate Plane Chapter 4: Solving Linear Equations Study Guide - Identify/graph ordered pairs Ex: Write the coordinates of - Identify the 4 quadrants point graphed and identify

More information

10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2

10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2 10-2 Circles Warm Up Lesson Presentation Lesson Quiz Holt Algebra2 2 Warm Up Find the slope of the line that connects each pair of points. 1. (5, 7) and ( 1, 6) 1 6 2. (3, 4) and ( 4, 3) 1 Warm Up Find

More information

Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations

Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations origin (x, y) Ordered pair (x-coordinate, y-coordinate) (abscissa, ordinate) x axis Rectangular or

More information

Notes Lesson 3 4. Positive. Coordinate. lines in the plane can be written in standard form. Horizontal

Notes Lesson 3 4. Positive. Coordinate. lines in the plane can be written in standard form. Horizontal A, B, C are Notes Lesson 3 4 Standard Form of an Equation: Integers Ax + By = C Sometimes it is preferred that A is Positive All lines in the plane can be written in standard form. Oblique Coordinate Horizontal

More information

Topic. Section 4.1 (3, 4)

Topic. Section 4.1 (3, 4) Topic.. California Standards: 6.0: Students graph a linear equation and compute the x- and y-intercepts (e.g., graph x + 6y = ). They are also able to sketch the region defined by linear inequality (e.g.,

More information

Exploring Slope. We use the letter m to represent slope. It is the ratio of the rise to the run.

Exploring Slope. We use the letter m to represent slope. It is the ratio of the rise to the run. Math 7 Exploring Slope Slope measures the steepness of a line. If you take any two points on a line, the change in y (vertical change) is called the rise and the change in x (horizontal change) is called

More information

0,0 is referred to as the end point.

0,0 is referred to as the end point. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Chapter 2: Radical Functions 2.1 Radical Functions and Transformations (Day 1) For the function y x, the radicand, x, must

More information

Test Name: Chapter 3 Review

Test Name: Chapter 3 Review Test Name: Chapter 3 Review 1. For the following equation, determine the values of the missing entries. If needed, write your answer as a fraction reduced to lowest terms. 10x - 8y = 18 Note: Each column

More information

Linear Topics Notes and Homework DUE ON EXAM DAY. Name: Class period:

Linear Topics Notes and Homework DUE ON EXAM DAY. Name: Class period: Linear Topics Notes and Homework DUE ON EXAM DAY Name: Class period: Absolute Value Axis b Coordinate points Continuous graph Constant Correlation Dependent Variable Direct Variation Discrete graph Domain

More information

Section 4.4: Parabolas

Section 4.4: Parabolas Objective: Graph parabolas using the vertex, x-intercepts, and y-intercept. Just as the graph of a linear equation y mx b can be drawn, the graph of a quadratic equation y ax bx c can be drawn. The graph

More information

We have already studied equations of the line. There are several forms:

We have already studied equations of the line. There are several forms: Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard

More information

notes13.1inclass May 01, 2015

notes13.1inclass May 01, 2015 Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard

More information

Sketching Straight Lines (Linear Relationships)

Sketching Straight Lines (Linear Relationships) Sketching Straight Lines (Linear Relationships) The slope of the line is m = y x = y 2 y 1 = rise run. Horizontal lines have the form y = b and have slope m = 0. Vertical lines have the form x = a and

More information

3.1. 3x 4y = 12 3(0) 4y = 12. 3x 4y = 12 3x 4(0) = y = x 0 = 12. 4y = 12 y = 3. 3x = 12 x = 4. The Rectangular Coordinate System

3.1. 3x 4y = 12 3(0) 4y = 12. 3x 4y = 12 3x 4(0) = y = x 0 = 12. 4y = 12 y = 3. 3x = 12 x = 4. The Rectangular Coordinate System 3. The Rectangular Coordinate System Interpret a line graph. Objectives Interpret a line graph. Plot ordered pairs. 3 Find ordered pairs that satisfy a given equation. 4 Graph lines. 5 Find x- and y-intercepts.

More information

Section 3.1 Objective 1: Plot Points in the Rectangular Coordinate System Video Length 12:35

Section 3.1 Objective 1: Plot Points in the Rectangular Coordinate System Video Length 12:35 Section 3.1 Video Guide The Rectangular Coordinate System and Equations in Two Variables Objectives: 1. Plot Points in the Rectangular Coordinate System 2. Determine If an Ordered Pair Satisfies an Equation

More information

Section 1.1 The Distance and Midpoint Formulas

Section 1.1 The Distance and Midpoint Formulas Section 1.1 The Distance and Midpoint Formulas 1 y axis origin x axis 2 Plot the points: ( 3, 5), (0,7), ( 6,0), (6,4) 3 Distance Formula y x 4 Finding the Distance Between Two Points Find the distance

More information

************************************** FINDING WAYS TO USE TECHNOLOGY TO ASSIST OUR STUDENTS WITH GRAPHING A VARIETY OF LINEAR EQUATIONS!!

************************************** FINDING WAYS TO USE TECHNOLOGY TO ASSIST OUR STUDENTS WITH GRAPHING A VARIETY OF LINEAR EQUATIONS!! ************************************** FINDING WAYS TO USE TECHNOLOGY TO ASSIST OUR STUDENTS WITH GRAPHING A VARIETY OF LINEAR EQUATIONS!! ************************************** PROJECT SUMMARY 1. Title

More information

+ b. From this we can derive the following equations:

+ b. From this we can derive the following equations: A. GEOMETRY REVIEW Pythagorean Theorem (A. p. 58) Hypotenuse c Leg a 9º Leg b The Pythagorean Theorem is a statement about right triangles. A right triangle is one that contains a right angle, that is,

More information

Class IX Mathematics (Ex. 3.1) Questions

Class IX Mathematics (Ex. 3.1) Questions Class IX Mathematics (Ex. 3.1) Questions 1. How will you describe the position of a table lamp on your study table to another person? 2. (Street Plan): A city has two main roads which cross each other

More information

6.7. Graph Linear Inequalities in Two Variables. Warm Up Lesson Presentation Lesson Quiz

6.7. Graph Linear Inequalities in Two Variables. Warm Up Lesson Presentation Lesson Quiz 6.7 Graph Linear Inequalities in Two Variables Warm Up Lesson Presentation Lesson Quiz 6.7 Warm-Up Tell whether the ordered pair is a solution of the equation. 1. x + 2y = 4; (2, 1) no 2. 4x + 3y = 22;

More information

We have already studied equations of the line. There are several forms:

We have already studied equations of the line. There are several forms: Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard

More information

Graphs and Linear Functions

Graphs and Linear Functions Graphs and Linear Functions A -dimensional graph is a visual representation of a relationship between two variables given by an equation or an inequality. Graphs help us solve algebraic problems by analysing

More information

Practice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise

Practice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise Practice Test (page 91) 1. For each line, count squares on the grid to determine the rise and the. Use slope = rise 4 Slope of AB =, or 6 Slope of CD = 6 9, or Slope of EF = 6, or 4 Slope of GH = 6 4,

More information

Slide 1 / 220. Linear Relations and Functions

Slide 1 / 220. Linear Relations and Functions Slide 1 / 220 Linear Relations and Functions Slide 2 / 220 Table of Contents Domain and Range Discrete v Continuous Relations and Functions Function Notation Linear Equations Graphing a Linear Equation

More information

Four Types of Slope Positive Slope Negative Slope Zero Slope Undefined Slope Slope Dude will help us understand the 4 types of slope

Four Types of Slope Positive Slope Negative Slope Zero Slope Undefined Slope Slope Dude will help us understand the 4 types of slope Four Types of Slope Positive Slope Negative Slope Zero Slope Undefined Slope Slope Dude will help us understand the 4 types of slope https://www.youtube.com/watch?v=avs6c6_kvxm Direct Variation

More information

Name: NOTES 5: LINEAR EQUATIONS AND THEIR GRAPHS. Date: Period: Mrs. Nguyen s Initial: LESSON 5.1 RATE OF CHANGE AND SLOPE. A. Finding rates of change

Name: NOTES 5: LINEAR EQUATIONS AND THEIR GRAPHS. Date: Period: Mrs. Nguyen s Initial: LESSON 5.1 RATE OF CHANGE AND SLOPE. A. Finding rates of change NOTES : LINEAR EQUATIONS AND THEIR GRAPHS Name: Date: Period: Mrs. Nguen s Initial: LESSON. RATE OF CHANGE AND SLOPE A. Finding rates of change vertical change Rate of change = = change in x The rate of

More information

Section 2.2 Graphs of Linear Functions

Section 2.2 Graphs of Linear Functions Section. Graphs of Linear Functions Section. Graphs of Linear Functions When we are working with a new function, it is useful to know as much as we can about the function: its graph, where the function

More information

JUST THE MATHS SLIDES NUMBER 5.2. GEOMETRY 2 (The straight line) A.J.Hobson

JUST THE MATHS SLIDES NUMBER 5.2. GEOMETRY 2 (The straight line) A.J.Hobson JUST THE MATHS SLIDES NUMBER 5.2 GEOMETRY 2 (The straight line) by A.J.Hobson 5.2.1 Preamble 5.2.2 Standard equations of a straight line 5.2.3 Perpendicular straight lines 5.2.4 Change of origin UNIT 5.2

More information

Geometry Unit 2: Linear. Section Page and Problems Date Assigned

Geometry Unit 2: Linear. Section Page and Problems Date Assigned Geometry Name: Geometry Unit 2: Linear Topics Covered: Midpoint formula Distance formula Slope Slope- Intercept Form Point- Slope Form Standard Form Assignment # Section Page and Problems Date Assigned

More information

Vocabulary Unit 2-3: Linear Functions & Healthy Lifestyles. Scale model a three dimensional model that is similar to a three dimensional object.

Vocabulary Unit 2-3: Linear Functions & Healthy Lifestyles. Scale model a three dimensional model that is similar to a three dimensional object. Scale a scale is the ratio of any length in a scale drawing to the corresponding actual length. The lengths may be in different units. Scale drawing a drawing that is similar to an actual object or place.

More information

Writing Equations of Parallel and Perpendicular Lines

Writing Equations of Parallel and Perpendicular Lines Writing Equations of Parallel and Perpendicular Lines The coordinate plane provides a connection between algebra and geometry. Postulates 17 and 18 establish a simple way to find lines that are parallel

More information

This assignment is due the first day of school. Name:

This assignment is due the first day of school. Name: This assignment will help you to prepare for Geometry A by reviewing some of the topics you learned in Algebra 1. This assignment is due the first day of school. You will receive homework grades for completion

More information

Revision Topic 11: Straight Line Graphs

Revision Topic 11: Straight Line Graphs Revision Topic : Straight Line Graphs The simplest way to draw a straight line graph is to produce a table of values. Example: Draw the lines y = x and y = 6 x. Table of values for y = x x y - - - - =

More information

Functions. Copyright Cengage Learning. All rights reserved.

Functions. Copyright Cengage Learning. All rights reserved. Functions Copyright Cengage Learning. All rights reserved. 2.2 Graphs Of Functions Copyright Cengage Learning. All rights reserved. Objectives Graphing Functions by Plotting Points Graphing Functions with

More information

AP Calculus Summer Review Packet

AP Calculus Summer Review Packet AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions

More information

Math 8 Honors Coordinate Geometry part 3 Unit Updated July 29, 2016

Math 8 Honors Coordinate Geometry part 3 Unit Updated July 29, 2016 Review how to find the distance between two points To find the distance between two points, use the Pythagorean theorem. The difference between is one leg and the difference between and is the other leg.

More information

Algebra II Notes Unit Two: Linear Equations and Functions

Algebra II Notes Unit Two: Linear Equations and Functions Syllabus Objectives:.1 The student will differentiate between a relation and a function.. The student will identify the domain and range of a relation or function.. The student will derive a function rule

More information

Math 154 Elementary Algebra. Equations of Lines 4.4

Math 154 Elementary Algebra. Equations of Lines 4.4 Math Elementary Algebra Caspers Name Date Equations of Lines. For each graph, solve each equation for y (if necessary), then write down the slope and y-intercept.. y x. y x - - - - - - - - - - - - - -

More information

A is any set of ordered pairs of real numbers. This is a set of ordered pairs of real numbers, so it is a.

A is any set of ordered pairs of real numbers. This is a set of ordered pairs of real numbers, so it is a. Fry Texas A&M University!! Math 150!! Chapter 3!! Fall 2014! 1 Chapter 3A Rectangular Coordinate System A is any set of ordered pairs of real numbers. A relation can be finite: {(-3, 1), (-3, -1), (0,

More information

Lesson 19: The Graph of a Linear Equation in Two Variables is a Line

Lesson 19: The Graph of a Linear Equation in Two Variables is a Line Lesson 19: The Graph of a Linear Equation in Two Variables is a Line Classwork Exercises Theorem: The graph of a linear equation y = mx + b is a non-vertical line with slope m and passing through (0, b),

More information

Classwork/Homework. Midterm Review. 1) 9 more than the product of a number and 12 2) 5 less than a number squared is twelve.

Classwork/Homework. Midterm Review. 1) 9 more than the product of a number and 12 2) 5 less than a number squared is twelve. Name: Classwork/Homework Midterm Review Verbal Expressions *Translate the words to math * *The word THAN changes the order of the terms *Square Root, Cube Root 3 *Squared x 2, Cubed x 3 *Quantity use parentheses!

More information

About Graphing Lines

About Graphing Lines About Graphing Lines TABLE OF CONTENTS About Graphing Lines... 1 What is a LINE SEGMENT?... 1 Ordered Pairs... 1 Cartesian Co-ordinate System... 1 Ordered Pairs... 2 Line Segments... 2 Slope of a Line

More information

.(3, 2) Co-ordinate Geometry Co-ordinates. Every point has two co-ordinates. Plot the following points on the plane. A (4, 1) D (2, 5) G (6, 3)

.(3, 2) Co-ordinate Geometry Co-ordinates. Every point has two co-ordinates. Plot the following points on the plane. A (4, 1) D (2, 5) G (6, 3) Co-ordinate Geometry Co-ordinates Every point has two co-ordinates. (3, 2) x co-ordinate y co-ordinate Plot the following points on the plane..(3, 2) A (4, 1) D (2, 5) G (6, 3) B (3, 3) E ( 4, 4) H (6,

More information

Section 2 0: The Rectangular Coordinate System. The Coordinate System

Section 2 0: The Rectangular Coordinate System. The Coordinate System Section 2 : The Rectangular Coordinate System The rectangular coordinate system is based on two number lines. A horizontal line called the x axis and a vertical line called the y axis. Each axis has marks

More information

Each point P in the xy-plane corresponds to an ordered pair (x, y) of real numbers called the coordinates of P.

Each point P in the xy-plane corresponds to an ordered pair (x, y) of real numbers called the coordinates of P. Lecture 7, Part I: Section 1.1 Rectangular Coordinates Rectangular or Cartesian coordinate system Pythagorean theorem Distance formula Midpoint formula Lecture 7, Part II: Section 1.2 Graph of Equations

More information

2 and 6 4 and 8 1 and 5 3 and 7

2 and 6 4 and 8 1 and 5 3 and 7 Geo Ch 3 Angles formed by Lines Parallel lines are two coplanar lines that do not intersect. Skew lines are that are not coplanar and do not intersect. Transversal is a line that two or more lines at different

More information

True/False. MATH 1C: SAMPLE EXAM 1 c Jeffrey A. Anderson ANSWER KEY

True/False. MATH 1C: SAMPLE EXAM 1 c Jeffrey A. Anderson ANSWER KEY MATH 1C: SAMPLE EXAM 1 c Jeffrey A. Anderson ANSWER KEY True/False 10 points: points each) For the problems below, circle T if the answer is true and circle F is the answer is false. After you ve chosen

More information

Lecture 4. If P1(x1,y1) and P2(x2,y2) are points on a non-vertical line, then the slope m of the line is defined by

Lecture 4. If P1(x1,y1) and P2(x2,y2) are points on a non-vertical line, then the slope m of the line is defined by Lines Lecture 4 In this section we shall discuss ways to measure the "steepness" or "slope" of a line in the plane. The ideas we develop here will be important when we discuss equations and graphs of straight

More information

Sect Linear Inequalities in Two Variables

Sect Linear Inequalities in Two Variables Sect 9. - Linear Inequalities in Two Variables Concept # Graphing a Linear Inequalit in Two Variables Definition Let a, b, and c be real numbers where a and b are not both zero. Then an inequalit that

More information

, use formula to find slope, m. * Given a graph of the line, use m or state that the slope is undefined.

, use formula to find slope, m. * Given a graph of the line, use m or state that the slope is undefined. Math A Eleentar Algebra Stud Guide for Ea Ea is scheduled for Wednesda, Noveber 9 th. You a use a " " note card (both sides) and a scientific calculator. You are epected to know (or have written on our

More information

x + 2 = 0 or Our limits of integration will apparently be a = 2 and b = 4.

x + 2 = 0 or Our limits of integration will apparently be a = 2 and b = 4. QUIZ ON CHAPTER 6 - SOLUTIONS APPLICATIONS OF INTEGRALS; MATH 15 SPRING 17 KUNIYUKI 15 POINTS TOTAL, BUT 1 POINTS = 1% Note: The functions here are continuous on the intervals of interest. This guarantees

More information

9.1 Linear Inequalities in Two Variables Date: 2. Decide whether to use a solid line or dotted line:

9.1 Linear Inequalities in Two Variables Date: 2. Decide whether to use a solid line or dotted line: 9.1 Linear Inequalities in Two Variables Date: Key Ideas: Example Solve the inequality by graphing 3y 2x 6. steps 1. Rearrange the inequality so it s in mx ± b form. Don t forget to flip the inequality

More information

Section 2.1 Graphs. The Coordinate Plane

Section 2.1 Graphs. The Coordinate Plane Section 2.1 Graphs The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of numbers to form

More information

Important Things to Remember on the SOL

Important Things to Remember on the SOL Notes Important Things to Remember on the SOL Evaluating Expressions *To evaluate an expression, replace all of the variables in the given problem with the replacement values and use (order of operations)

More information

Graphing Equations Case 1: The graph of x = a, where a is a constant, is a vertical line. Examples a) Graph: x = x

Graphing Equations Case 1: The graph of x = a, where a is a constant, is a vertical line. Examples a) Graph: x = x 06 CHAPTER Algebra. GRAPHING EQUATIONS AND INEQUALITIES Tetbook Reference Section 6. &6. CLAST OBJECTIVE Identif regions of the coordinate plane that correspond to specific conditions and vice-versa Graphing

More information

MATH 90 CHAPTER 3 Name:.

MATH 90 CHAPTER 3 Name:. MATH 90 CHAPTER 3 Name:. 3.1 Reading Graphs & Plotting Points Need to Know Reading Graphs and Charts (Bar, Pie, Line) Plotting Points and Ordered Pairs and the Coordinate System Bar Graphs Data Source:

More information

Chapter P: Preparation for Calculus

Chapter P: Preparation for Calculus 1. Which of the following is the correct graph of y = x x 3? E) Copyright Houghton Mifflin Company. All rights reserved. 1 . Which of the following is the correct graph of y = 3x x? E) Copyright Houghton

More information

Mini-Lecture 3.1 Graphing Equations

Mini-Lecture 3.1 Graphing Equations Copyright 0 Pearson Education, Inc. Mini-Lecture. Graphing Equations. Plot ordered pairs.. Determine whether an ordered pair of numbers is a solution to an equation in two variables.. Graph linear equations.

More information

WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING)

WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) 1 Contents Some Simple Straight Lines y = mx + c Parallel Lines Perpendicular Lines Plotting Equations Shaded Regions Credits WJEC Question

More information

Section 2.0: Getting Started

Section 2.0: Getting Started Solving Linear Equations: Graphically Tabular/Numerical Solution Algebraically Section 2.0: Getting Started Example #1 on page 128. Solve the equation 3x 9 = 3 graphically. Intersection X=4 Y=3 We are

More information

Unit 2A: Systems of Equations and Inequalities

Unit 2A: Systems of Equations and Inequalities Unit A: Systems of Equations and Inequalities In this unit, you will learn how to do the following: Learning Target #1: Creating and Solving Systems of Equations Identify the solution to a system from

More information

In math, the rate of change is called the slope and is often described by the ratio rise

In math, the rate of change is called the slope and is often described by the ratio rise Chapter 3 Equations of Lines Sec. Slope The idea of slope is used quite often in our lives, however outside of school, it goes by different names. People involved in home construction might talk about

More information

2.1 Solutions to Exercises

2.1 Solutions to Exercises Last edited 9/6/17.1 Solutions to Exercises 1. P(t) = 1700t + 45,000. D(t) = t + 10 5. Timmy will have the amount A(n) given by the linear equation A(n) = 40 n. 7. From the equation, we see that the slope

More information

Algebra I Notes Unit Six: Graphing Linear Equations and Inequalities in Two Variables, Absolute Value Functions

Algebra I Notes Unit Six: Graphing Linear Equations and Inequalities in Two Variables, Absolute Value Functions Sllabus Objective.4 The student will graph linear equations and find possible solutions to those equations using coordinate geometr. Coordinate Plane a plane formed b two real number lines (axes) that

More information

Relations and Functions 2.1

Relations and Functions 2.1 Relations and Functions 2.1 4 A 2 B D -5 5 E -2 C F -4 Relation a set of ordered pairs (Domain, Range). Mapping shows how each number of the domain is paired with each member of the range. Example 1 (2,

More information