Chapter 2: Linear Equations and Functions

Transcription

1 Chapter 2: Linear Equations and Functions

2 Chapter 2: Linear Equations and Functions Assignment Sheet Date Topic Assignment Completed 2.1 Functions and their Graphs and 2.2 Slope and Rate of Change 2.1 and 2.2 Homework Day Functions and their Graphs and 2.2 Slope and Rate of Change 2.1 and 2.2 Homework Day 2 MATCH THE GRAPH SLOPE ACTIVITY Complete the Match the Graph worksheet for homework. 2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines Homework 2.3 and 2.4 More on 2.4 Why write equations of lines? pg. 97 #59-65 More on 2.4 Practice 2.4C (19-24) 2.5 Scatter Plots and Correlation - Use Hoola- Hoop activity to collect linear data. NO HOMEWORK Regression Lines using the Graphing Calculator 2.5 Homework 2.6 Linear Inequalities in Two Variables 2.6 Homework 2.7 Graphing Piecewise Functions 2.7 Homework (day 1) 2.7 Graphing and Writing Piecewise Functions 2.7 Homework (day 2) Absolute Value Exploration with Desmos Complete the activity in class. 2.8 Absolute Value Graphs 2.8 Homework Review Review EXAM Multiple Choice Review Worksheet pg. 130 # 1-25 pg. 133 # 1-24, 27 Chapter 2 Keystones Worksheet

3 Functions and Their Graphs and 2.2- Slope and Rate of Change RECALL from Algebra I: coordinate plane Cartesian plane or x-y plane ordered pairs points in the form (x, y) -5 x-coordinate first value in an ordered pair, usually referred to as the also called the y-coordinate the second value in an ordered pair, usually referred to as the also called the Slope - a numerical value that represents the steepness of a line (m) Slope = m = vertical change rise = horizontal change run Slopes of Graphs s( y) = The slope of a line passing through the points ( x1, y1) and ( x2, y2 ) is y2 y1 m = x x Find the slope of the line passing through the points and tell whether it rises, falls, is horizontal, or vertical. 1 3 a.) (4, 2) (-18, 1) b.) (-7, 3) (-2, 3) c.), 1,

4 function a set of ordered pairs for which there is exactly one y-value for each x-value. A function passes the. Circle the graphs that represent a function. Applications: 1. You work at the local dairy queen and get paid $8.50 per hour. An equation modeling the money that you earn would be y = $8.50x where y equals the amount you get paid for working x hours. Create an x-y table of values and graph them below. x (hours) y (dollars) Connect the points with a line. What does the slope of the line represent?

5 2. A water park slide drops 8 feet over a horizontal distance of 24 feet. a. Find its slope. b. Find the drop over a 54-foot section with the same slope. 3. The slope of a road, or grade, is usually expressed as a percent. For example, if a road has a grade of 3%, it rises 3 feet for every 100 feet of horizontal distance. a. Find the grade of a road that rises 75 feet over a horizontal distance of 2000 feet. b. Find the horizontal length of a road with a grade of 4% if the road rises 50 feet over its length.

6 4. The heights and ages of the players on a basketball team are shown in the graph below. Is height a function of age? 5. A cyclist maps her ride using an iphone App that provides her with graphs of the elevation along the ride. She notices a pretty steep section around the 5-mile point. a.) Use the graphs below to determine the grade of the road that she traveled near the 5-mile point.

7 b.) Use the graph above to determine the average speed of the cyclist during the first 20 minutes of her ride. SAT Type Problem: Find the value of k so that the line through the given points has the given slope. 1.) (5, k) and (k, 7), m=1 2.) (-2, k) and (k, 4), m=3

8 HOMEWORK 2.1/2.2 DAY 1 Read the article at describing the rise of T-mobile. Under the heading How big is the gap between the two? there is a description of how quickly T-mobile is growing relative to Sprint and AT&T. Use the data in the paragraph to create a graph of the three companies starting with the end of the second quarter of this year (July, 2014) showing their total customers and projected rates of growth. Does the prediction of T-mobile passing AT&T in a little over two years seem plausible? Summarize the data from the article: Summarize the rates of growth listed in the article: Create a graph for all three carriers. Plot time on the x-axis and number of customers on the y-axis.

9 MATCH THE GRAPH SLOPE ACTIVITY An exploration with the CBR units and graphing calculators Calculator Instructions : APPS Easy Data Setup 1 (Dist), enter change units to feet, OK Setup 3 (Distance Match) Start OK Next Start (when you are ready to match the graph) 1.) Sketch a graph of the graph that you were trying to match a.)what variable is being represented on the y-axis? (label this) units? b.)what variable is being represented on the x-axis? (label this) units? c.) What does the y-intercept represent? Try a second time to match the graph that you sketched by hitting the retry key on the calculator.

10 2.) Hit the new button on the graphing calculator to generate a different graph and then sketch the graph below Hit the retry button to perfect your matching of the graph. Discuss the different properties of your graph below : 3.) Hit the new button on the graphing calculator to generate a different graph and then sketch the graph below Hit the retry button to perfect your matching of the graph. Discuss the different properties of your graph below:

11 FOLLOW UP QUESTIONS: 1.) What does the slope of the line represent in each graph? a.) What does a positive slope represent in the context of your graph? b.) What does a negative slope represent in the context of your graph? c.) What does a zero slope (horizontal line) represent in the context of your graph? d.) If the slope of one line is steeper than another, what does that indicate in the context of your graph? 2.) How did you know how far from the wall to stand when you originally looked at the graph?

12 2.1/2.2 Homework Day 2 Identify the domain and range. Graph the relation. Then tell whether the relation is a function. Domain: Function? Range: Use the vertical line test to determine whether the relation is a function. Function? Evaluate the following functions. f (x) = 2 3 x 2 x + 5; f (6) f (x) = 3 + 4x; f 1 2 Estimate the slope of the line. m = m = m =

13 Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal or vertical. (-10, -12) and (2, -6) (-1,4) and (-2,4) (0, 7 2 ) and ( 2, 5 2 ) Which of the above lines is the steepest? Application You are in charge of building a wheel chair ramp for a doctor s office. Federal regulations require that the ramp must extend 12 inches for every 1 inch of rise. The ramp needs to be a height of 18 inches. a.) How far should the end of the ramp be from the base of the building? b.) Use the Pythagorean Theorem to determine the length of the ramp. Find the value of k so that the line through the given points has the given slope. (-3, 2k) and (k,6), m=4 (9, -k) and (3k, -1), m = 1 3

14 2.3- Quick Graphs of Linear Equations and 2.4- Writing Equations of Lines Notes The SLOPE INTERCEPT form of a line is: STANDARD FORM OF A LINE: Ax + By = C where A, B, and C are and A The X-INTERCEPT of a line is where. To find the x-intercept,. y = 2x + 3 y = 2 3 x 3 y = 2 5 x x-intercept: x-intercept: x-intercept: Standard Form: Standard Form: Standard Form: What formula can you use to generalize the slope of a line if the equation is given in standard form? m = 5x + 3y = -15 slope: y-intercept: x-intercept: y = 3x y = 7 x = 4

15 Graph then write an equation of the line that passes through the point ( -3, 4) and A.) Slope-Intercept Form: y = mx + b 2 m = 3 B.) Point-Slope Form: y y1 = m( x x1 ) C.) Standard Form: Ax + By = C 1) Write the equation of a line that passes through the point (2,3) and a slope of 1 2 2) Write the equation of the ling that passes through the point (7,-4) and m = 2 5 Given Two Points: Write the equation of the line that passes through ( 2, 1) and (3,4)

16 1) Write the equation of the line shown. State your answer in slope-intercept Form. 2) Write an equation of the line that passes through the points (2,0) and (4,- 6) 3) Given the points (- 8,8) and (0,1), write the equation of the line. Writing Equations of Parallel and Perpendicular Lines Parallel Lines: Two lines are parallel if and only if they have the same. Perpendicular lines: Two lines are perpendicular if and only if their slopes are AND of each other. Key Questions: All types of vertical lines are parallel to what types of lines? All types of vertical lines are perpendicular to what types of lines?

17 Graph and use the slope formula tell whether the lines are parallel, perpendicular or neither. Line 1: through ( 3,3) and (3, 1) Line 2: through ( 2, 3) and (2,3) Write an equation of the line that passes through (2, -3) and is parallel to the line that passes through (3, 5) and (-1, -3) Write an equation of the line that passes through (3, 2) and is perpendicular to the line y = 3 x + 2

18 Write an equation of a line that passes through (3, -5) that is a) perpendicular and b) parallel to the line x = 4. Then graph each line on the graph provided. a.) perpendicular b.) parallel Why write equations of lines? Create a graph to represent the data given below regarding college tuition for out of state students at the University of Michigan. Based on the observed rate of growth, what will it cost to attend the University of Michigan ten years from now? Cost for two semesters year $12, $28, Thousands Of $ 60 5 years since 1990

19 Direct Variation The variables x and y show direction variation given the following equation is true: where. EX: y = 5x k is the of. Y-intercept is equal to zero The graph goes through the origin EX: The variables x and y vary directly, and when y = 12, x = 4. Write then graph the equation that relates x and y. Find y when x = 5 EX: Using what you k now about the equations of lines and the graphs of direct variation, decide if the equation represents direct variation. A.) 2y 5x = 0 B.) 3y 7 = 10x EX: Write and graph a direct variation equation that has the given ordered pair as a solution: (6, -2)

20 EX: Tell whether the data shows direct variation. Length, x (inches) Price, y (dollars) 14 Karat Gold Chains (1 gram per inch) EX: In a recipe for cookies, the amount of flour varies directly wit the amount of butter. The recipe calls for 4 cups of flour and 2/3 cup of butter. What is the constant of variation? Write and equation representing how the flour, f, varies directly wit the butter, b. EX: The amount of sales tax that you pay in the state of Illinois varies directly wit the price of the item. The sales tax on clothing is 6.25%. Write an equation involving direct variation to represent the tax charged for an item of clothing. What does k represent if you equation?

21 2.3 and 2.4 Homework 1.) Graph the following equations, find their x- intercept, and then write the equation in standard form. y = 5x +1 y = 5 4 x + 2 y = 3 4 x 1 4 x-intercept: x-intercept: x-intercept: Standard Form: Standard Form: Standard Form: 2.) Find the slope of the equation 5x 2y = 20. Find the intercepts and then graph the equation. Slope: x-intercept: y-intercept: 3.) Write the equation of the line that passes through the point (7,- 4) and has a slope of 2 5.

22 4.) Write the equation of the line that passes through the point (- 6,5) and has a slope of 0. 5.) Write an equation of the line that passes through (1, - 1) and is perpendicular to the line y = 1 2 x ) Write an equation of the line that passes through (6, - 10) and is perpendicular to the line that passes through (4,- 6) and (3,- 4). 7.) Write an equation of the line that passes through (2,- 7) and is parallel to the line x=5.

23 8.) Write an equation of the line that passes through (4,6) and is parallel to the line that passes through (6,- 6) and (10,- 4). 9.) Write an equation of the line shown. 10.) Write the equation of the line that passes through the points (2,0) and (4,-6)

24 HOOLA HOOP CHALLENGE In class, we collected data for the amount of time for a hoola hoop pass. Please list the data in the given table. # of People Time Elapsed 1.) Which variable is independent? 2.) Which variable is dependent? 3.) Which axis should the independent variable be on? 4.) Which axis should the dependent variable be on? PLOT the above ordered pairs using the scatter plot feature of your graphing calculator. Describe the correlation of the data: Derive the equation of the best fit line from your graphing calculator: FOLLOW UP QUESTIONS: 1.) Interpret the slope of your regression line in terms of # of people and time elapsed. 2.) Interpret the y-intercept of your regression line in terms of # of people and time elapsed. 3.) From the information collected, can you predict how long it would take 10 people to complete the hoola hoop pass? Is this an example of interpolation or extrapolation? 4.) From the information collected, can you predict how long it would take 30 people to complete the hoola hoop pass? Is this an example of interpolation or extrapolation? 5.) How many people could have been involved in the activity if the hoola hoop pass took 72 seconds? 6.) Do you find any real life conditions in this experiment that will impact our predictions?

25 2.5- Correlation and Best-Fitting Lines Scatter Plot: a graph of a set of data pairs (x,y) Positive Correlation: y tends to as x increases Negative Correlation: y tends to as x increases NO Correlation: the points show 1.) Think of two variables that have a positive correlation: 2.) Think of two variables that have a negative correlation: REGENTS SCORE VS. STUDY HOURS Calculate the Best Fit Line by Hand: y = Study Regents Score Hours Find the BEST best-fitting line using your graphing calculator : y = The independent variable is and the dependent variable is Use interpolation to predict a student s regents score if they studied for 4 hours Interpret the slope of the regression lines in terms of hours of study and regents score.

26 Creating a Scatter Plot and Regression Line in your Calculator ENTER THE DATA: STAT 1:EDIT ENTER Enter the data into your lists SET UP THE SCATTER PLOT: 2 ND Y= ENTER Set up Plot 1 as shown below: SET UP THE WINDOW: 2 ND WINDOW Choose window settings that fit the min and max values of your data in the lists. Remember the x-values are in List 1 and the y-values are in List 2. CREATE THE SCATTER PLOT: GRAPH CREATE THE LINEAR REGRESSION MODEL: STAT CALC 4:LinReg(ax+b) ENTER ENTER Record your equation, then go to the Y= screen and graph the equation. Y= enter the equation (the variable x is just below the MODE button) GRAPH

27 2.5 Homework The table below gives the average life expectancy (in years) of a person based on various years of birth. Let x represent the number of years since (x = 10 represents the year 1910) Year of Birth (x) Life Expectancy (y) a.) Graph the data below (be sure to scale and label your axes appropriately). Draw in an estimate of the best fit line. Find two points on the line and estimate the equation for the best fit line without a calculator. Equation of best fit line from graph (no calculator): y = SHOW WORK! b.) Graph a scatterplot of the data on your graphing calculator. Find the equation of the best fit line from your graphing calculator. Equation of best fit line from calculator: y = c.) Use the equation from your calculator to predict the life expectancy for someone born in d.) The independent variable is. The dependent variable is e.) Interpret the slope in terms of year of birth and life expectancy.

28 The Stroop Test One of the main uses of data is to make predictions about real-world situations. We are going to perform an experiment from cognitive psychology, which is the branch of psychology that tries to understand and explain how the human brain works. The experiment is named after the man who first performed it, J.E. Stroop. Each student will look at a list of words written in color red, green, black, or blue. Each list is different in length. The student will be asked to say the color of the ink for each word. Three timers will record the time needed to complete each list and the average noted. Two different lists will be used. One in which the color of the ink matches the color of the word, for example, red written in red ink; and a second where the color of the ink does not match the color of the word, for examples, red written in blue ink. The first type is called matching, the second, non-matching. Answer the following questions before we begin: 1.) What do you think we ll find when we perform these experiments? How will the matching data differ from the non-matching data? 2.) What question would a cognitive psychologist be trying to answer by performing these experiments? Matching List Length Time Non-Matching List Length Time

29 Graphing Calculators Use the graphing calculator to perform a linear regression of time vs. list length for matching data. Repeat for the non-matching data. Matching: Non-matching: Discussion 1.) Interpret the slope and y-intercept of the matching linear regression line. In what units are they measured? What would these points mean to a cognitive psychologist? 2.) Making predictions: Use your equation to estimate how long it would take to name the colors in a list of 10 matching words. How long would it take for 25 words? Which is an example of extrapolation and which is an example of interpolation? 3.) Explain why you must be careful when extrapolating. 4.) Interpret the slope and y-intercept of the non-matching linear regression line. In what units are they measured? What would these points mean to a cognitive psychologist? 5.) What conclusions would a cognitive psychologist draw from this experiment?

30 2.6- Linear Inequalities in Two Variables Warm Up: Check whether the given ordered pair is a solution of 2x 3y 5 1.) (-2, -5) 2.) (2,1) 3.) (-4, -1) ACTIVITY: 1.) Solution (color): Not a Solution (color): 2.) Test the following ordered pairs in the inequality x + y 1 Then plot them in accordance with the color-coding that you defined in 1. (0, 0) ( 2,0) (4,0) (-2,0) (-4, 0) (0,2) (2,2) (4,2) (-2,2) (-4, 2) (0, 4) (2,4) (4,4) (-2, 4) (-4,4) (0, -2) (2,-2) (4, -2) (-2,-2) (-4, -2) (0, -4) (2, -4) (4,-4) (-2, -4) (-4,-4)

31 What is the case about the points on the line x + y = 1? Describe a general strategy for graphing an inequality in two variables. Graph the following inequalities: 5x 2y 4 y < 2x y < -2 x 1

32 2.6 Homework Check whether the given ordered pairs are solutions of the inequality. y < 9x + 7; (3, 8) x 5; ( 5,1) Match the inequality with its graph. 1.) 2x y 4 2.) 2x y < 4 3.) 2x + y 4 Graph the following inequalities on the coordinate plane 9x 2y 18 6x 1 3 y x + y < 0 5x > 20 Write the inequality whose graph is shown.

33 2.7- Piecewise Functions What is a piecewise function? 1) f ( 1) = f ( 5) = f ( 4) = 2) f ( 2) = f ( 1) = f ( 0) =

34 3) f ( 6) = f ( 2) = f ( 10) = 4) f ( 4) = f ( 0) = f ( 3) = 5) f ( 3) = f ( 4) =

35 2.7 Homework Day 1 Evaluate the function for the given value of x. f(-4)= f(0)= f(-2)= f(5)= Graph the following functions.

36 2.7 Homework Day 2 Write equations for the piecewise functions whose graph is shown.

37 Exploring Graphs of Absolute Value Functions in Desmos Start up: 1) Open the Desmos app on your ipad 2) Enter in the equation y = a x h + k 3) Add sliders to all three variables a, h, and k Begin: Adjust the sliders to that a = 1, h = 0 and k = 0. The sliders a, h and k represent the constants in the equation q(x). 1) Write the equation of the graph. (This is the parent function for the family of absolute value functions) 2) Fill out the table of values that corresponds with the function by reading the values from the graph. x f(x) 3) What is the shape of the graph? 4) Where is the vertex of the graph? Name the coordinates. 5) Adjust the sliders so that a = 1, h = 2, and k = 3. Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph 6) Adjust the sliders so that a = 4, h = 2, and k = 3. Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph 7) Adjust the sliders so that a = -4, h = 2, and k = 3. Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph

38 8) Adjust the sliders so that a = 3, h = -4, and k = -1. Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph 1 9) Adjust the sliders so that a =, h = -2, and k = Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph 10) Adjust the sliders so that a = 1, h = -3, and k = 4. 5 Where is the vertex of the new graph? Write the new equation of the graph: What are the slopes of the branches of the new graph? Describe the translation of the parent function to attain the new graph Select the blue dot on the slider that corresponds with parameter a. Describe the two things that happen to the graph as you change parameter a. 1.) 2.) What special property does the graph have when a = 0? Select the blue dot on the slider that corresponds with parameter h. What happens to the graph as you change the parameter h? What special property does the graph have when h = 0?

39 Select the blue dot on the slider that corresponds with parameter k. What happens to the graph as you change the parameter k? What special property does the graph have when k = 0? Describe your findings. What does each variable a, h, and k represent? How does changing each change the look of the graph? Be specific and use examples.

40 2.8 Absolute Value Functions (Group Work Discovery Activity) General Graphing Form: y = a x h + k Use the table of values below in order to graph y = x. X y Use the table of values to graph the following equations 1.) y = x + 1 X y A.) Describe the translation of this graph from y = x : It is a shift of. B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry:

41 2.) y = x + 1 X y A.) Describe the translation of this graph from y = x It is a shift of. B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry: 3.) y = x 1 X y A.) Describe the translation of this graph from y = x It is a shift of B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry:

42 4) y = x 1 x y A.) Describe the translation of this graph from y = x : It is a shift of B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry: 5) y = x x y A.) Describe the translation of this graph from y = x : It is a about the B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry:

43 6.) y = 3 x x y A.) How does this graph compare to y = x? B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry: 1 7.) y = x 2 X y A.) How does this graph compare to y = x? B.) Left slope: Right slope: C.) Vertex: D.) Axis of Symmetry:

44 Using the equations from numbers 1-7 organize the equations into the appropriate categories. Original absolute value function: Horizontal Shift Graphs Vertical Shift Graphs Flipped Graphs Wider or More Narrow Graphs In all of the above equations where are the slopes located? 2. Predict the transformation for the following graphs then use a table to verify the graph by graphing with a table. 1.) y = x A.) Horizontal shift? B.) Vertical Shift? C.) Direction opens? Wider or more narrow? X y

45 Predict the transformation for the following graphs then use a table to verify the graph by graphing with a table. 2) y = 2 x A.) Horizontal shift? B.) Vertical Shift? C.) Direction opens? Wider or more narrow X y Predict the transformation for the following graphs then use a table to verify the graph by graphing with a table. 1 3) y = x 2 A.) Horizontal shift? 2 B.) Vertical Shift? C.) Direction opens? Wider or more narrow? X y

46 2.8 Homework Graph the function and describe the translation of the parent function y = x to attain the graph. y = 6 x 7 y = x + 9 y = x 8 +1 Translation of y = x Translation of y = x Translation of y = x y = x y = 1 3 x y = 1 2 x + 6 Translation of y = x Translation of y = x Translation of y = x

47 Write an equation of the graph shown.

48 1 Algebra II Chapter 2 Review Sheet 1. Given g(x) = x 2 + 3x 5, what is g( 2)? a. -7 b. -1 c. 5 d. -3 e What is the slope of the line passing through the points (-5, 4) and (-1, 8)? a. -2/3 b. -1 c. 3/2 d. 1 e. 2/3 3. What is the slope of the line passing through the points (2, 5) and (-4, 3)? a. 1/3 b. 3 c. -3 d. -1/3 e Which of the following lines is the steepest? a. Line 1 through (4, 5) and (3, 2) b. Line 2 through (6, 4) and (3, 2) c. Line 3 through (-2, 7) and (6, 6) d. Line 4 through (-1, 3) and (4, 5) e. Line 5 through (-2, -4) and (1, 2) 5. Thie line that passes through the points (3, 0) and (-5, 8) : a. is vertical b. falls c. is horizontal d. rises e. doesn t exist 6. A ladder 40 feet in length that hits the wall at a height of 24 feet has a slope of: a. ¾ b. 4/3 c. 3/5 d. 5/3 e. 4/5 7. What is the slope of the line y = 1 5 x 7? a. 1/5 b. -7 c. -5 d. -1/5 e What is the y-intercept of the line y = 2 3 x + 4 5? a. 2/3 b. 4/5 c. -4/5 d. -2/3 e. 5/4

49 9. What is the x-intercept of the line y = 1 4 x 16? a. -1/4 b. -16 c. 64 d. 4 e What is the y-intercept and the x-intercept of the line y = 5x 15? a. y-intercept = 15, x-intercept = -5 b. y-intercept = -15, x-intercept = -3 c. y-intercept = 15, x-intercept = -3 d. y-intercept = 15, x-intercept = 3 e. y-intercept = -5, x-intercept = Which function is represented by the graph shown at right? a. 2x 4y = 8 b. 2x + 4y = 8 c. 2x 4y = 8 d. 2x 4y = 8 e. 2x 4y = What is the equation of the line that passes through the point (1,5) and has a slope of -3? a. y = 3x + 8 b. y = 3x 2 c. y = 3x 8 d. y = 3x + 8 e. y = 3x What is the equation of the line that passes through the point (-2, -3) and has a slope of 4? a. y = 4x + 5 b. y = 4x +11 c. y = 4x + 5 d. y = 4x 11 e. y = 4x What is the equation of the line that passes through the point (-1, 7) and is parallel to the line y = 2x 1? a. y = 1 2 x b. y = 1 2 x c. y = 2x + 5 d. y = 2x 9 e. y = 2x + 5

50 15. What is the equation of the line that passes through the point (6, -3) and is perpendicular to the line y = 1 3 x + 4? a. y = 3x +15 b. y = 3x 15 c. y = 3x +15 d. y = 1 3 x 5 e. y = 1 3 x If y tends to increase as x increases on a scatter plot, what is the correlation of the paired data? a. positive b. negative c. relatively no correlation d. undefined e. none 17. Which is the best fitting line for the data shown? X Y a. y = 0.51x b. y = 0.051x c. y = 5.1x d. y = 0.51x e. y = x Which of the ordered pairs is a solution of the inequality 2x 5y 8? a. (2, -5) b. (0, -3) c. (-1, -2) d. (5, 0) e. (-2, -5) 19. Which of the ordered pairs is not a solution of x < y + 3? a. (-3, -5) b. (0, 2) c. (-2, 0) d. (2, 2) e. (-1, 3) 20. Given f (x) = 4x +1, 2x 3, x < 1 x 1, what is f ( 1)? a. -5 b. 3 c. -1 d. -3 e Given f (x) = 5, 3 < x < 0 3, 0 x 1 7, 1 < x < 4, what is f (1)? a. -5 b. 1 c. 0 d. 7 e. 3

51 22. Which function is represented by the graph shown at right? a. y = 2x 1 b. y = 2x +1 c. y = 2x 1 d. y = 2x 1 e. y = 2x Which statement is true about the graph of the function y = x 7 + 3? a. Its vertex is at (0, 10) b. Its vertex is at (-7, 3) c. Its vertex is at (3, 7) d. Its vertex is at (10, 0) e. Its vertex is at (7, 3) 24. Given f (x) = x, 1 x 0 x, 0 < x 1 2x, 1 < x 2, what is f 1 2? a. -1 b. 2 c. ½ d. -2 e. -1/2 25. Which function is represented by the graph shown? a. y = 3x + 2 b. y = 2 3x c. y = 3x + 2 d. y = 3x + 2 e. y = 3x What is the equation of the line passing through the point (-1, 3) with a slope of 1/2? a. (y 3) = 1 2 (x +1) b. (y + 3) = 1 (x +1) 2 c. (y 3) = 1 2 (x 1) d. (y + 3) = 1 (x 1) e. none of the above 2

52 27. Determine the Standard Form of the equation y = 2x + 3. a. (y 3) = 2(x + 0) b. (y + 3) = 2(x + 0) c. 2x + y = 3 d. 2x + y = 3 e. y = 1 2 x Which equation form does NOT describe a linear function? a. y = mx + b b. Ax + By = C c. y = x h + k d. (y y 1 ) = m(x x 1 )