WRITING AND GRAPHING LINEAR EQUATIONS ON A FLAT SURFACE #1313
|
|
|
- Clifford McDonald
- 5 years ago
- Views:
Transcription
1 WRITING AND GRAPHING LINEAR EQUATIONS ON A FLAT SURFACE #11 SLOPE is a number that indicates the steepness (or flatness) of a line, as well as its direction (up or down) left to right. SLOPE is determined b the ratio: vertical change horizontal change between an two points on a line. For lines that go up (from left to right), the sign of the slope is positive. For lines that go down (left to right), the sign of the slope is negative. An linear equation written as = m + b, where m and b are an real numbers, is said to be in SLOPE-INTERCEPT FORM. m is the SLOPE of the line. b is the Y-INTERCEPT, that is, the point (0, b) where the line intersects (crosses) the -ais. If two lines have the same slope, then the are parallel. Likewise, PARALLEL LINES have the same slope. Two lines are PERPENDICULAR if the slope of one line is the negative reciprocal of the slope of the other line, that is, m and! 1 m. Note that m! "1 ( m ) = "1. Eamples: and! 1,! and, 4 and! 4 Two distinct lines that are not parallel intersect in a single point. See "Solving Linear Sstems" to review how to find the point of intersection. Also see the tetbook, pages 0, 8, 91, 98, 01, 07-08, and 14. Eample 1 Write the slope of the line containing the points (-1, ) and (4, ). First graph the two points and draw the line through them. (4,) Look for and draw a slope triangle using the two given points. Write the ratio triangle:. vertical change in horizontal change in using the legs of the right (-1,) Assign a positive or negative value to the slope (this one is positive) depending on whether the line goes up (+) or down ( ) from left to right. If the points are inconvenient to graph, use a "Generic Slope Triangle", visualizing where the points lie with respect to each other. 6 Etra Practice 006 CPM Educational Program. All rights reserved.
2 Eample Graph the linear equation = Using = m + b, the slope in = is 4 7 and the -intercept is the point (0, ). To graph, begin at the vertical change -intercept (0, ). Remember that slope is horizontal change so go up 4 units (since 4 is positive) from (0, ) and then move right 7 units. This gives a second point on the graph. To create the graph, draw a straight line through the two points Eample A line has a slope of 4 and passes through (, ). What is the equation of the line? Using = m + b, write = + b. Since (, ) represents a point (, ) on the line, 4 substitute for and for, = ( 4 ) + b, and solve for b. = b! " 9 4 = b! " 1 4 = b. The equation is = 4! 1 4. Eample 4 Decide whether the two lines at right are parallel, perpendicular, or neither (i.e., intersecting). First find the slope of each equation. Then compare the slopes. 4 = -6 and -4 + =. 4 = -6-4 = - 6 = = 4 + The slope of this line is = = 4 + = 4 + = 4 + The slope of this line is 4. These two slopes are not equal, so the are not parallel. The product of the two slopes is 1, not -1, so the are not perpendicular. These two lines are neither parallel nor perpendicular, but do intersect. ALGEBRA Connections CPM Educational Program. All rights reserved.
3 Eample Find two equations of the line through the given point, one parallel and one perpendicular to the given line: =! + and (-4, ). For the parallel line, use = m + b with the same slope to write =! + b. Substitute the point ( 4, ) for and and solve for b. =! (!4) + b " = 0 + b "! = b Therefore the parallel line through (-4, ) is =!!. For the perpendicular line, use = m + b where m is the negative reciprocal of the slope of the original equation to write = + b. Substitute the point ( 4, ) and solve for b. = (!4) + b " = b Therefore the perpendicular line through (-4, ) is = +. Write the slope of the line containing each pair of points. 1. (, 4) and (, 7). (, ) and (9, 4). (1, -) and (-4, 7) 4. (-, 1) and (, -). (-, ) and (4, ) 6. (8, ) and (, ) Use a Generic Slope Triangle to write the slope of the line containing each pair of points: 7. (1, 40) and (, 7) 8. (0, 49) and (4, 90) 9. (10, -1) and (-61, 0) Identif the -intercept in each equation. 10. = =!! 1. + = 1 1. = = = 1 Write the equation of the line with: 16. slope = 1 and passing through (4, ). 17. slope = and passing through (-, -). 18. slope = - 1 and passing through (4, -1). 19. slope = -4 and passing through (-, ). 8 Etra Practice 006 CPM Educational Program. All rights reserved.
4 Determine the slope of each line using the highlighted points Using the slope and -intercept, determine the equation of the line Graph the following linear equations on graph paper. 7. = = = 4 0. = = 1 State whether each pair of lines is parallel, perpendicular, or intersecting.. = and = + 4. = 1 + and = = and + =. = -1 and + = 6. + = 6 and =! 1! 7. + = 6 and + = = and 4 = = 1 and 4 = + 7 Find an equation of the line through the given point and parallel to the given line. 40. = and (-, ) 41. = 1 + and (-4, ) 4. = and (-, ) 4. = -1 and (-, 1) = 6 and (-1, 1) 4. + = 6 and (, -1) = and (1, -1) = 1 and (4, -) ALGEBRA Connections CPM Educational Program. All rights reserved.
5 Find an equation of the line through the given point and perpendicular to the given line. 48. = and (-, ) 49. = 1 + and (-4, ) 0. = and (-, ) 1. = -1 and (-, 1). + = 6 and (-1, 1). + = 6 and (, -1) 4. 4 = and (1, -1). 4 = 1 and (4, -) Write an equation of the line parallel to each line below through the given point (-,) - (,8) (-8,6) (-,) - (7,4) - (-,-7) - 0 Etra Practice 006 CPM Educational Program. All rights reserved.
6 Answers ! ! 16 9 ( ) 10. (0, ) 11. 0,! 4.! (0, 6) 1. (0, 1) 14. (0, ) 1. (0, ) 16. = = 18. =! =!4! 7 0.! =! 4. =! +. = =! line with slope 1 and -intercept (0, ) 8. line with slope! and -intercept (0, 1) 9. line with slope 4 and -intercept (0, 0)! 0. line with slope 6 and -intercept # 0, 1 $ & 1. line with slope! " % and -intercept (0, 6). parallel. perpendicular 4. perpendicular. perpendicular 6. parallel 7. intersecting 8. intersecting 9. parallel 40. = = = + 4. = = = = = = = = = - 1. = + 4. = 7 6. = = = = ALGEBRA Connections CPM Educational Program. All rights reserved.
SLOPE A MEASURE OF STEEPNESS through 7.1.5
SLOPE A MEASURE OF STEEPNESS 7.1. through 7.1.5 Students have used the equation = m + b throughout this course to graph lines and describe patterns. When the equation is written in -form, the m is the
SLOPE A MEASURE OF STEEPNESS through 2.1.4
SLOPE A MEASURE OF STEEPNESS 2.1.2 through 2.1.4 Students used the equation = m + b to graph lines and describe patterns in previous courses. Lesson 2.1.1 is a review. When the equation of a line is written
Lines and Their Slopes
8.2 Lines and Their Slopes Linear Equations in Two Variables In the previous chapter we studied linear equations in a single variable. The solution of such an equation is a real number. A linear equation
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
Tangent line problems
You will find lots of practice problems and homework problems that simply ask you to differentiate. The following examples are to illustrate some of the types of tangent line problems that you may come
REVIEW, pages
REVIEW, pages 69 697 8.. Sketch a graph of each absolute function. Identif the intercepts, domain, and range. a) = ƒ - + ƒ b) = ƒ ( + )( - ) ƒ 8 ( )( ) Draw the graph of. It has -intercept.. Reflect, in
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
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
Geometry CP Constructions Part I Page 1 of 4. Steps for copying a segment (TB 16): Copying a segment consists of making segments.
Geometry CP Constructions Part I Page 1 of 4 Steps for copying a segment (TB 16): Copying a segment consists of making segments. Geometry CP Constructions Part I Page 2 of 4 Steps for bisecting a segment
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
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
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
5 and Parallel and Perpendicular Lines
Ch 3: Parallel and Perpendicular Lines 3 1 Properties of Parallel Lines 3 Proving Lines Parallel 3 3 Parallel and Perpendicular Lines 3 Parallel Lines and the Triangle Angles Sum Theorem 3 5 The Polgon
Advanced Algebra. Equation of a Circle
Advanced Algebra Equation of a Circle Task on Entry Plotting Equations Using the table and axis below, plot the graph for - x 2 + y 2 = 25 x -5-4 -3 0 3 4 5 y 1 4 y 2-4 3 2 + y 2 = 25 9 + y 2 = 25 y 2
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
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
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
Graphs, Linear Equations, and Functions
Graphs, Linear Equations, and Functions. The Rectangular R. Coordinate Fractions Sstem bjectives. Interpret a line graph.. Plot ordered pairs.. Find ordered pairs that satisf a given equation. 4. Graph
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)
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
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
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.
Outputs. Inputs. the point where the graph starts, as we ll see on Example 1.
We ve seen how to work with functions algebraically, by finding domains as well as function values. In this set of notes we ll be working with functions graphically, and we ll see how to find the domain
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
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.
Section 3.1: Introduction to Linear Equations in 2 Variables Section 3.2: Graphing by Plotting Points and Finding Intercepts
Remember to read the tetbook before attempting to do our homework. Section 3.1: Introduction to Linear Equations in 2 Variables Section 3.2: Graphing b Plotting Points and Finding Intercepts Rectangular
Transformation of curve. a. reflect the portion of the curve that is below the x-axis about the x-axis
Given graph of y f = and sketch:. Linear Transformation cf ( b + a) + d a. translate a along the -ais. f b. scale b along the -ais c. scale c along the y-ais d. translate d along the y-ais Transformation
(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2
.5 Equations of Parallel and Perpendicular Lines COMMON CORE Learning Standards HSG-GPE.B.5 HSG-GPE.B. Essential Question How can ou write an equation of a line that is parallel or perpendicular to a given
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
7.6 Solve Linear Systems of
7.6 Solve Linear Sstems of Linear Inequalities Goal p Solve sstems of linear inequalities in two variables. Your Notes VOCABULARY Sstem of linear inequalities Solution of a sstem of linear inequalities
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
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,
Geometry Unit 5 Geometric and Algebraic Connections. Table of Contents
Geometry Unit 5 Geometric and Algebraic Connections Table of Contents Lesson 5 1 Lesson 5 2 Distance.p. 2-3 Midpoint p. 3-4 Partitioning a Directed Line. p. 5-6 Slope. p.7-8 Lesson 5 3 Revisit: Graphing
Parallel lines are lines that never intersect and are always the same distance apart. Parallel Lines
Lesson 4.6 Objectives Determine if two lines are parallel or perpendicular. Write equations of parallel and perpendicular lines. Slopes of Parallel and Perpendicular Lines Parallel and perpendicular lines
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
Unit 6: Connecting Algebra and Geometry Through Coordinates
Unit 6: Connecting Algebra and Geometry Through Coordinates The focus of this unit is to have students analyze and prove geometric properties by applying algebraic concepts and skills on a coordinate plane.
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 - - - - - - - - - - - - - -
of Straight Lines 1. The straight line with gradient 3 which passes through the point,2
Learning Enhancement Team Model answers: Finding Equations of Straight Lines Finding Equations of Straight Lines stud guide The straight line with gradient 3 which passes through the point, 4 is 3 0 Because
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.
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
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,
0 COORDINATE GEOMETRY
0 COORDINATE GEOMETRY Coordinate Geometr 0-1 Equations of Lines 0- Parallel and Perpendicular Lines 0- Intersecting Lines 0- Midpoints, Distance Formula, Segment Lengths 0- Equations of Circles 0-6 Problem
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
Example 1: Use the graph of the function f given below to find the following. a. Find the domain of f and list your answer in interval notation
When working with the graph of a function, the inputs (the elements of the domain) are always the values on the horizontal ais (-ais) and the outputs (the elements of the range) are always the values on
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
.(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,
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),
Area of triangle? Area of square? Area of Rectangle? distance formula: slope point form: slope intercept form: February 22, 2017
Formula Page for this Unit! Quiz tomorrow! Slope Formula: rise run slope intercept form: slope point form: distance formula: Area of triangle? Area of parallelogram? Area of square? Area of Rectangle?
Domain: The domain of f is all real numbers except those values for which Q(x) =0.
Math 1330 Section.3.3: Rational Functions Definition: A rational function is a function that can be written in the form P() f(), where f and g are polynomials. Q() The domain of the rational function such
GEOMETRY APPLICATIONS
GEOMETRY APPLICATIONS Chapter 3: Parallel & Perpendicular Lines Name: Teacher: Pd: 0 Table of Contents DAY 1: (Ch. 3-1 & 3-2) SWBAT: Identify parallel, perpendicular, and skew lines. Identify the angles
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
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
Time To Hit The Slopes. Exploring Slopes with Similar Triangles
Time To Hit The Slopes Eploring Slopes with Similar Triangles Learning Goals In this lesson, ou will: Use an equation to complete a table of values. Graph an equation using a table of values. Use transformations
Section 4.3 Features of a Line
Section.3 Features of a Line Objectives In this section, ou will learn to: To successfull complete this section, ou need to understand: Identif the - and -intercepts of a line. Plotting points in the --plane
Linear Functions. College Algebra
Linear Functions College Algebra Linear Function A linear function is a function whose graph is a straight line. Linear functions can be written in the slope-intercept form of a line: f(x) = mx + b where
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 +
4.4 Absolute Value Equations. What is the absolute value of a number? Example 1 Simplify a) 6 b) 4 c) 7 3. Example 2 Solve x = 2
4.4 Absolute Value Equations What is the absolute value of a number? Eample Simplif a) 6 b) 4 c) 7 3 Eample Solve = Steps for solving an absolute value equation: ) Get the absolute value b itself on one
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
Inclination of a Line
0_00.qd 78 /8/05 Chapter 0 8:5 AM Page 78 Topics in Analtic Geometr 0. Lines What ou should learn Find the inclination of a line. Find the angle between two lines. Find the distance between a point and
Mathematics (www.tiwariacademy.com)
() Miscellaneous Exercise on Chapter 10 Question 1: Find the values of k for which the line is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin. Answer 1: The given
3.2 Exercises. rise y (ft) run x (ft) Section 3.2 Slope Suppose you are riding a bicycle up a hill as shown below.
Section 3.2 Slope 261 3.2 Eercises 1. Suppose ou are riding a biccle up a hill as shown below. Figure 1. Riding a biccle up a hill. a) If the hill is straight as shown, consider the slant, or steepness,
Section 4.2 Graphs of Exponential Functions
238 Chapter 4 Section 4.2 Graphs of Eponential Functions Like with linear functions, the graph of an eponential function is determined by the values for the parameters in the function s formula. To get
CHAPTER - 10 STRAIGHT LINES Slope or gradient of a line is defined as m = tan, ( 90 ), where is angle which the line makes with positive direction of x-axis measured in anticlockwise direction, 0 < 180
Intensive Math-Algebra I Mini Lesson MA.912.A.3.10
Intensive Math-Algebra I Mini Lesson M912.3.10 Summer 2013 Writing Equations of Perpendicular Lines Student Packet Day 10 Name: Date: Benchmark M912.3.10 Write an equation of a line given any of the following
7h2 Graphing Basic Rational Functions (Gebrochenrationaler Funktionen)
7h Graphing Basic Rational Functions (Gebrochenrationaler Funktionen) Goals: Graph rational functions Find the zeros and y-intercepts Identify and understand the asymptotes Match graphs to their equations
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: a b 1.
ASSIGNMENT ON STRAIGHT LINES LEVEL 1 (CBSE/NCERT/STATE BOARDS) 1 Find the angle between the lines joining the points (0, 0), (2, 3) and the points (2, 2), (3, 5). 2 What is the value of y so that the line
4.1 The Coordinate Plane
4. The Coordinate Plane Goal Plot points in a coordinate plane. VOCABULARY Coordinate plane Origin -ais -ais Ordered pair -coordinate -coordinate Quadrant Scatter plot Copright McDougal Littell, Chapter
Algebra I. Linear Equations. Slide 1 / 267 Slide 2 / 267. Slide 3 / 267. Slide 3 (Answer) / 267. Slide 4 / 267. Slide 5 / 267
Slide / 67 Slide / 67 lgebra I Graphing Linear Equations -- www.njctl.org Slide / 67 Table of ontents Slide () / 67 Table of ontents Linear Equations lick on the topic to go to that section Linear Equations
Geometry CP. Unit 1 Notes
Geometry CP Unit 1 Notes 1.1 The Building Blocks of Geometry The three most basic figures of geometry are: Points Shown as dots. No size. Named by capital letters. Are collinear if a single line can contain
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,.
Also available in Hardcopy (.pdf): Coordinate Geometry
Multiple Choice Practice Coordinate Geometry Geometry Level Geometry Index Regents Exam Prep Center Also available in Hardcopy (.pdf): Coordinate Geometry Directions: Choose the best answer. Answer ALL
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
1) y = 2x 7 2) (-2, 3) ( 3, -1) 3) table. 4) y 5 = ½ ( x 4) 5) 2x + 4y = 7 6) y = 5 7) 8) 9) (-1, 5) (0, 4) 10) y = -3x 7. 11) 2y = -3x 5 12) x = 5
I SPY Slope! Geometr tetbook 3-6, pg 165 (), pg 172 (calculator) Name: Date: _ Period: Strategies: On a graph or a table rise ( Δ) Slope = run Δ ( ) Given 2 points Slope = 2 2 In an equation 1 1 1) = 2
AICE Mathematics AS Level Summer Review
AICE Mathematics AS Level Summer Review Welcome to AICE mathematics. This is a rigorous and fast paced course so it is important to make sure that you have mastered the prerequisite skills. These necessary
GEOMETRY LAB UNIT 3: PARALLEL AND PERPENDICULAR LINES
GEOMETRY LAB UNIT 3: PARALLEL AND PERPENDICULAR LINES **SHOW ALL WORK** A COMPASS AND GRAPH PAPER IS NECESSARY FOR THIS UNIT LESSON TOPIC BOOK/ VIDEO DAY 1 LINES AND ANGLES (3-1) SYSTEMS OF EQUATIONS (P152-3)
Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompan Intermediate Algebra, 3rd edition Miller, O'Neill, & Hde Prepared b Stephen Toner Victor Valle College Last updated: 7/8/14 2.1 The Rectangular
Linear Equations in Two Variables
Section. Linear Equations in Two Variables Section. Linear Equations in Two Variables You should know the following important facts about lines. The graph of b is a straight line. It is called a linear
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.,
Parallel and Perpendicular Lines. What are the slope and y-intercept of each equation?
6 6-6 What You ll Learn To determine whether lines are parallel To determine whether lines are And Wh To use parallel and lines to plan a bike path, as in Eample Parallel Lines Parallel and Perpendicular
List of Topics for Analytic Geometry Unit Test
List of Topics for Analytic Geometry Unit Test 1. Finding Slope 2. Rule of 4 (4 forms of a line) Graph, Table of Values, Description, Equation 3. Find the Equations- Vertical and Horizontal Lines 4. Standard
Algebra I Notes Slope Unit 04a
OBJECTIVE: F.IF.B.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over
SYSTEMS OF LINEAR EQUATIONS
SYSTEMS OF LINEAR EQUATIONS A system of linear equations is a set of two equations of lines. A solution of a system of linear equations is the set of ordered pairs that makes each equation true. That is
Bell Ringer Write each phrase as a mathematical expression. Thinking with Mathematical Models
Bell Ringer Write each phrase as a mathematical expression. 1. the sum of nine and eight 2. the sum of nine and a number 3. nine increased by a number x 4. fourteen decreased by a number p 5. the product
1. A(-2, 2), B(4, -2) 3 EXAMPLE. Graph the line y = Move up 3 units. Quick Check See left.
-. Plan Objectives To graph lines given their equations To write equations of lines Eamples Graphing Lines in Slope- Intercept Form Graphing Lines Using Intercepts Transforming to Slope- Intercept Form
Lesson 8.1 Exercises, pages
Lesson 8.1 Eercises, pages 1 9 A. Complete each table of values. a) -3 - -1 1 3 3 11 8 5-1 - -7 3 11 8 5 1 7 To complete the table for 3, take the absolute value of each value of 3. b) - -3 - -1 1 3 3
3.5 Write and Graph Equations
.5 Write and Graph Equations of Lines Goal p Find equations of lines. Your Notes VOCABULARY Slope-intercept form Standard form Eample Write an equation of a line from a graph Write an equation of the line
Distance. Dollars. Reviewing gradient
Gradient The gradient of a line is its slope. It is a very important feature of a line because it tells you how fast things are changing. Look at the graphs below to find the meaning of gradient in two
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.
Intro. To Graphing Linear Equations
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 shortest distance from point K to line is the length of a segment perpendicular to from point K. Draw a perpendicular segment from K to.
8. Find the distance between each pair of parallel lines with the given equations. Copy each figure. Construct the segment that represents the distance indicated. 12. K to The shortest distance from point
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
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
Writing Linear Functions
2- Writing Linear Functions Objectives Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Vocabulary Point-slope form Why learn this? When
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
Algebra II Honors Summer Packet Summer 2017
Algebra II Honors Summer Packet Summer 2017 Name: The following packet contains content that you should have learned in previous Mathematics courses. You will be expected to demonstrate proficiency with
L13-Mon-3-Oct-2016-Sec-1-1-Dist-Midpt-HW Graph-HW12-Moodle-Q11, page 1 L13-Mon-3-Oct-2016-Sec-1-1-Dist-Midpt-HW Graph-HW12-Moodle-Q11
L13-Mon-3-Oct-016-Sec-1-1-Dist-Midpt-HW11-1--Graph-HW1-Moodle-Q11, page 1 L13-Mon-3-Oct-016-Sec-1-1-Dist-Midpt-HW11-1--Graph-HW1-Moodle-Q11 1.1 Rectangular Coordinate System: Suppose we know the sum of
You MUST know the big 3 formulas!
Name 3-13 Review Geometry Period Date Unit 3 Lines and angles Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation y = mx + b Writing the equation of a line given
Learning Objectives for Section Graphs and Lines. Cartesian coordinate system. Graphs
Learning Objectives for Section 3.1-2 Graphs and Lines After this lecture and the assigned homework, ou should be able to calculate the slope of a line. identif and work with the Cartesian coordinate sstem.
Did you ever think that a four hundred year-old spider may be why we study linear relationships today?
Show Me: Determine if a Function is Linear M8221 Did you ever think that a four hundred year-old spider may be why we study linear relationships today? Supposedly, while lying in bed Rene Descartes noticed
College Prep Algebra II Summer Packet
Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When