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Unit 3 Check Sheet Name ______________________________Per______

Linear Functions (Print)

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Section HMK 3.1 Rate of Change and Slope

Worksheet 3.1 #1-15 all

3.3 Slope-Intercept Form Worksheet 3.3 #1-23 all or Math XL

Quiz 1

Stacking Cups

3.3B Horizontal and Vertical Shifts Worksheet 3.3B In Class Activity Worksheet 3.3B HW #1-7all

3.4 Point Slope Form Worksheet 3.4 #1-21 all

3.5 Standard Form Worksheet 3.5 #1-27 all

3.5B Switching Between the Forms Worksheet 3.5B #1-8 all

3.6 Slopes of Parallel and Perpendicular Lines Worksheet 3.6 #1-22 all or Math XL

Quiz 2

Review Review Worksheet #1-21 all

Unit 3 Pre-Assessment

Unit Test

Quiz 1: _______ Score/Possible

Quiz 2: _______ Score/Possible

Pre-Test: _______ Score/Possible

Total Quiz Ratio: _______ Total Score/Total Possible

Name: ______________________________________ Date: _________________ Period: ___________________

1

Math 1 Unit 3.1 Homework Use the following charts to answer the questions. 1. 2. 3.

a) What is the average rate of a) What is the average rate of a) What is the average rate of change of goals between change of miles between change of cars between Game 1 and Game 2? 1 gallon and 3 gallons? Hour 1 and Hour 2? _______________________ _______________________ _______________________

b) What is the average rate of b) What is the average rate of b) What is the average rate of change of goals between change of miles between change of cars between Game 1 and Game 3? 3 gallons and 7 gallons? Hour 1 and Hour 4? _______________________ _______________________ _______________________

Find the slope of each line. 4. 5. 6.

m = _________________ m = _________________ m = _________________ 7. 8. 9.

m = _________________ m = _________________ m = _________________

Find the slope of the line that passes through each pair of points. 10. (2, 1), (0, 0) m = _____________ 11. (4, 5), (6, 2) m = _____________ 12. (3, 8), (7, 3) m = _____________ 13. (1, 0), (−4, 2) m = _____________ 14. (8,−4), (−6,−3) m = _________ 15. (−2,−3), (6, 5) m = ___________

Name Class Date 3.3 Practice Form K Slope-Intercept Form Find the slope and y-intercept of the graph of each equation.

1. y = – 2x + 7 2. y = 6x + 11

3. y = –7x – 8 4. y = –2.5x + 3.2

5. y = –9 6. y = 14

x – 27

Write an equation of a line with the given slope m and y-intercept b.

7. m = –5, b = –6 8. m = 1, b = –4

9. m = 0.4, b = –9 10. m = 0, b = 3

Write an equation in slope-intercept form of each line.

11. 12.

Write an equation in slope-intercept form of the line that passes through the given points.

13. (–1, 2) and (0, 0) 14. (–2, 9) and (1, 6)

15. (12, 10) and (16, 8) 16. (–4, –1) and (–8, 7)

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Class Date Practice (continued) Form K Slope-Intercept Form Graph each equation. 17. y = x – 2 18. y = 3x + 1

19. y = –x – 1 20. y = –3x – 2

21. y = 12

x + 2 22. y = –45

x – 5

23. A car is traveling at 45 mi/h. Write an equation that models the total distance

d traveled after h hours. What is the graph of the equation?


Math 1 Unit 3.3b Homework Name ______________________________________ Period ________________ Student should be able to complete this assignment with NO graphing calculator or graphing utility.

In order to label equations, we will use f(x), g(x) or any other letter in order to label the function.

1. On the graph below, graph and label f(x) = 3x, g(x) = 3x + 2, and h(x) = 3x - 4.

1a. Name 2 things these functions have in common and why.

_________________________________________________________________

_________________________________________________________________

b. Name 2 things about these functions that are different and why.

_________________________________________________________________

_________________________________________________________________

c. What can you do to f(x) = 3x to graph g(x) = 3x + 2? ______________________________________________________

d. What can you do to f(x) = 3x to graph h(x) = 3x – 4? ______________________________________________________

2. For 𝑓𝑓(𝑥𝑥) = −14𝑥𝑥 and 𝑔𝑔(𝑥𝑥) = −1

4𝑥𝑥 + 2

a. graph f(x) and then graph g(x) by shifting f(x) b. Graph g(x) by stating the slope and y intercept and using that information to graph g(x)

m = b =

2c. Compare the graphs of g(x) in 2a and 2b. What are the similarities and what are the differences? ______________

__________________________________________________________________________________________________ 3. On the graph below, graph and label 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 + 2, 𝑔𝑔(𝑥𝑥) = 1

3 𝑥𝑥 + 2,𝑎𝑎𝑎𝑎𝑎𝑎 ℎ(𝑥𝑥) = 3𝑥𝑥 + 2

3a. Name 2 things these functions have in common and why.

_________________________________________________________________

_________________________________________________________________

3b. Name 2 things about these functions that are different and why.

_________________________________________________________________

_________________________________________________________________

c. What can you do to 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 + 2 to graph 𝑔𝑔(𝑥𝑥) = 13

𝑥𝑥 + 2 ? ____________________________________________

d. What can you do to 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 + 2 to graph ℎ(𝑥𝑥) = 3𝑥𝑥 + 2 ? _____________________________________________

Math 1 Unit 3.3b Homework page 2 4. With NO graphing utility, graph and label 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| , 𝑔𝑔(𝑥𝑥) = |𝑥𝑥| + 3 𝑎𝑎𝑎𝑎𝑎𝑎 ℎ(𝑥𝑥) = |𝑥𝑥| − 2 on the same graph. 4a. Explain how to graph 𝑔𝑔(𝑥𝑥) 𝑎𝑎𝑎𝑎𝑎𝑎 ℎ(𝑥𝑥) using 𝑓𝑓(𝑥𝑥).

___________________________________________

___________________________________________

___________________________________________

___________________________________________

5. With NO graphing utility, graph and label 5a. 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| , 𝑔𝑔(𝑥𝑥) = |𝑥𝑥 + 3| 5b. 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| , 𝑔𝑔(𝑥𝑥) = |𝑥𝑥 + 1| + 4 5c. 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| , 𝑎𝑎𝑎𝑎𝑎𝑎 ℎ(𝑥𝑥) = |𝑥𝑥 − 2| Graph 𝑔𝑔(𝑥𝑥) by moving 𝑓𝑓(𝑥𝑥) 𝑔𝑔(𝑥𝑥) = |𝑥𝑥 − 2| − 3

Explain how to graph 𝑔𝑔(𝑥𝑥) and left 1 unit and up 4 units Graph 𝑔𝑔(𝑥𝑥) by moving 𝑓𝑓(𝑥𝑥)

ℎ(𝑥𝑥) from 𝑓𝑓(𝑥𝑥) _______________ right 2 units and down 3 units

____________________________

6. The graph of 𝑓𝑓(𝑥𝑥) = 𝑥𝑥2 is below. On the bottom 7. The graph of 𝑓𝑓(𝑥𝑥) is shown below. On the

Graph, sketch 𝑔𝑔(𝑥𝑥) = 𝑥𝑥2 − 3 bottom graph, sketch 𝑓𝑓(𝑥𝑥) + 2

x f(x) -2 -1 0 1 2

Math 1 Unit 3.3b Name ______________________________________ Period ________________ In class activity and students need graphing calculators or access to desmos.com or another graphing utility.

In order to label equations, we will use f(x), g(x) or any other letter in order to label the function rule.

1. On the same screen, graph and label f(x) = x + 3, g(x) = 2x + 3, and h(x) = 12x + 3. Copy your graphs below.

1a. What is the y intercept for f(x) __________ g(x) __________ h(x) _________

b. Which graph is the steepest? ________

c. Which graph is the least steep? _________

2. Match the equation with the best choice for its graph. A. 𝑦𝑦 = 1

4 𝑥𝑥 − 2 Graph # _____ B. 𝑦𝑦 = 4 𝑥𝑥 − 2 Graph # _____ C. 𝑦𝑦 = 𝑥𝑥 − 2 Graph # _____

3. For the form 𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏, how does the changing value of 𝑚𝑚 affect the graph of the equation.

_______________________________________________________________________________________________ 4. On the same screen, graph and label 𝑓𝑓(𝑥𝑥) = −2𝑥𝑥 + 4 , 𝑔𝑔(𝑥𝑥) = −2𝑥𝑥 − 4 𝑎𝑎𝑎𝑎𝑎𝑎 ℎ(𝑥𝑥) = −2𝑥𝑥 + 2. Copy your

graphs below.

4a. What is the y intercept for f(x) __________ g(x) __________ h(x) _________

4b. What is the x intercept for

f(x) __________ g(x) __________ h(x) _________

4c. What do the graphs have in common?

____________________________________________________

5. Match the equation with the best choice for its graph. A. 𝑦𝑦 = 1

3 𝑥𝑥 − 3 Graph # _____ B. 𝑦𝑦 = 1

3 𝑥𝑥 + 1 Graph # _____ C. 𝑦𝑦 = 1

3 𝑥𝑥 Graph # _____

# 1 # 2 # 3

# 1 # 2 # 3

Math 1 Unit 3.3b In class activity 6. For the form 𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏, how does the changing value of 𝑏𝑏 affect the graph of the equation.

_______________________________________________________________________________________________ 7. By completing a table and plotting the 8. Using a graphing utility, graph 𝑦𝑦 = |𝑥𝑥|

points graph 𝑦𝑦 = |𝑥𝑥|

x y -2 -1 0 1 2

9. On the same screen, graph and label f(x) = |𝑥𝑥|, g(x) = |𝑥𝑥| + 2, and h(x) =|𝑥𝑥| − 4. Copy your graphs below.

9a. What are the y intercepts for f(x) __________ g(x) __________ h(x) _________

9b. What are the x intercepts for

f(x) __________ g(x) __________ h(x) _________

9c. For the form, y = |𝑥𝑥| + 𝑘𝑘, what does the value of 𝑘𝑘 do to

y = |𝑥𝑥| ? _________________________________________

10. On the same screen, graph and label 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| and 𝑔𝑔(𝑥𝑥) = |𝑥𝑥 + 2| and ℎ(𝑥𝑥) = |𝑥𝑥 − 3| 10a. What are the y intercepts for f(x) ____________ g(x) ____________ h(x) ___________

10b. What are the x intercepts for

f(x) ____________ g(x) ____________ h(x) ___________

10c. For the form, y = |𝑥𝑥 + ℎ|, what does the value of ℎ do to

y = |𝑥𝑥| ? _________________________________________

11. With NO graphing utility: a. Graph and label 𝑓𝑓(𝑥𝑥) = |𝑥𝑥| b. What do you have to do to 𝑓𝑓(𝑥𝑥) to graph 𝑔𝑔(𝑥𝑥) = |𝑥𝑥| − 2 ?

____________________________________________________ c. Graph and label 𝑔𝑔(𝑥𝑥) = |𝑥𝑥| − 2 d. What do you have to do to 𝑓𝑓(𝑥𝑥) to graph ℎ(𝑥𝑥) = |𝑥𝑥 + 1 | ?

_____________________________________________________ e. Graph and label ℎ(𝑥𝑥) = |𝑥𝑥 + 1|

Name Class Date 3.4 Practice Form K Point-Slope Form Write an equation in point-slope form of the line that passes through the given point and has the given slope.

1. (1, 3); m = 5 2. (–2, –1); m = –3 3. (4, –7); m = –14

Graph each equation.

4. y + 1 = 3(x – 2) 5. y – 4 = –1(x + 2) 6. y – 3 = –2(x + 4)

Graph the line that passes through the given point and has the given slope m.

7. (–1, –3); m = 2 8. (–3, –2); m = –4 9. (–2, 6); m = –12

10. Open-Ended Write an equation in each of the following forms that has a

slope of – 23

.

a. point-slope form b. slope-intercept form

11. Writing Describe what you know about the graph of a line represented by the equation y + 4 = –5(x – 1).


Name Class Date Practice (continued) Form K Point-Slope Form Model the data in each table with a linear equation in point-slope form. What does the slope represent? 12. 13.

Write an equation in point-slope form of each line. 14. 15.

Write an equation in point-slope form of the line that passes through the given points. Then write the equation in slope-intercept form. 16. (5, 1), (0, 2) 17. (–2, –3), (4, 3)

18. (–3, –2), (2, 3) 19. (2, 5), (8, –7)

20. Writing Describe how you would use the point-slope form to write the equation of a line that passes through the points (2, 3) and (–1, 6) in slope-intercept form.

21. A restaurant’s goal is to serve 600 customers in 8 hours and 900 customers in 12 hours. Write an equation in point-slope form that represents the number of customers served per hour. What is the graph of the equation?


Name Class Date 3.5 Practice Form K Standard Form Find the x- and y-intercepts of the graph of each equation. 1. x + y = –3 2. 2x – 4y = –8

3. x + 5y = –10

4. –3x + 2y = 12 Draw a line with the given intercepts.

5. x-intercept: 2 y-intercept: –3

6. x-intercept: –4 y-intercept: –2

Graph each equation using x- and y-intercepts. 7. 3x + y = –2 8. –2x + y = 1 9. x – y = 4

10. –6x + y = –4 11. 2x – 3y = –6 12. 6x + 8y = 24

For each equation, tell whether its graph is a horizontal or a vertical line.

13. x = –1 14. y = 5

Graph each equation. 15. x = –5 16. y = 4


x y

0

0

x y

0

0

x y

0

0

x y 0

0

Name Class Date Practice (continued) Form K Standard Form 17. Writing Explain how y – 2 = 2(x + 6) can be rewritten into standard form.

Then show your work in transforming the equation to standard form.

Write each equation in standard form using integers. 18. y = x + 6 19. y + 5 = –(x + 3)

20. y – 1 = –12

(x – 4) 21. y = –23

x + 6

22. You work two jobs. At the first job, you earn $10 per hour. At the

second job, you earn $12 per hour. You earned $60 last week. Write and graph an equation that represents this situation. What are two combinations of hours you could have worked at each job?

23. Mike was the kicker for the football team. He scored 9 points during a game kicking field goals (3 points) and extra points (1 point). Write and graph an equation that represents this situation. What are two combinations of field goals x and extra points y he could have made?

For each graph, find the x- and y-intercepts. Then write an equation in standard form using integers. 24. 25.

Find the x- and y-intercepts of the line that passes through the given points. 26. (2, –2), (6, –4) 27. (–1, –3), (4, 2)


Name _____________________________________________ Date _______________________ Period _________

Unit 3.5B Worksheet Use the given information to fill in the rest of the empty boxes

Point Slope Form Slope-Intercept Form Standard Form Ordered Pair(s) & Slope 1.

𝑦𝑦 − 4 = 5(𝑥𝑥 − 8)

2.

𝑦𝑦 = 𝑥𝑥 − 4

(2,−2)

3.

2𝑥𝑥 − 3𝑦𝑦 = 6

(9,4)

4.

(4,−2), (5,−4)

5.

𝑦𝑦 = −35𝑥𝑥 + 2

(10,−4)

6.

3𝑥𝑥 − 5𝑦𝑦 = 15

(20,9)

7. 𝑦𝑦 + 6 = −3(𝑥𝑥 + 1)

8.

(−6,3), 𝑚𝑚 = 23

Name Class Date 3.6 Practice Form K Slopes of Parallel and Perpendicular Lines Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. 1. (–1, 3); y = 2x – 8 2. (2, 6); y = –3x + 5

3. (–3, 12); y = – 13

x + 7 4. (8, –10); y = 34

x + 1

Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain.

5. y = –5x + 9

5x + y = –21

6. x = 1

10

y = 1

10

7. y = –4x + 14

–x + 4y= 14 8. y =

67

x + 4

y = –67

x – 5

Determine whether each statement is always, sometimes, or never true. Explain. 9. Two lines with different slopes are parallel.

10. Two lines with the same y-intercept are perpendicular.

11. Two lines whose slopes are opposites of each other are perpendicular.


Name Class Date Practice (continued) Form K Slopes of Parallel and Perpendicular Lines Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation.

12. (6, –2); y = –3x + 4 13. (2, 7); y = 12

x – 11

14. (–5, –6); x + y = 6 15. (4, –5); 2x + 2y = 6

16. Open-Ended Write the equations of three lines whose graphs are parallel to y = 2x + 11.

17. Open-Ended Write the equations of two lines whose graphs are

perpendicular to y = – 13

x – 9.

18. What is the slope of a line that is parallel to y = 2?

19. What is the slope of a line that is perpendicular to y = 2?

20. What is the slope of a line that is parallel to x = –4?

21. What is the slope of a line that is perpendicular to x = –4?

22. On a map, Center St. passes through coordinates (5, –3) and (3, 7). Merrie Rd. intersects Center St. and passes through coordinates (2, 6) and (–3, 5). Are these streets perpendicular? Explain.


Name _______________________________________ Period ______ Math 1 – Unit 3 Test Review 1. Find the slope of the line that passes through the points (-5, 6) and (3,7). 2. Write the equation of the line in point-slope form that has a slope of -5 and passes through (-7, -11). 3. Change the equation in Problem #2 to slope-intercept form. 4. Find the x- and y-intercepts for -5x +10y = -30. 5. Find the y-intercept for y = |x - 3|. 6. Are the following lines parallel, perpendicular, or neither? 4x – 5y = 6

y – 3 = 4 ( 2)5

x +

7. Which of the following is a solution to f(x) = 3 35

x − ? Choose ALL that apply.

a. (10, 1)

b. (0, 3) c. (0, -3) d. (10, 3)

8. The following represents a linear function showing the distance Bob has travelled. a. Find the slope. b. Find the average rate of change between hours 1 and 5. 9. Values for the linear function f(x) are shown.

x f(x) 3 -13 4 -8 5 -3

a. Find the average rate of change. b. Find the slope from x = 3 to x = 5.

Time (Hrs) 1 3 5 7 Miles 45 135 225 315

10. Graph f(x) = 3 34

x− +

11. Find the slope of the line that passes through (-5, -3) and (-3, 2). Graph the line and name one other

point on the line. 12. Write the equation of the line that passes through (-8, 20) and is perpendicular to y = 4x + 3. Put your

final answer in slope intercept form. 13. Change to slope intercept form and graph 3x – 9y = 18

14. Find the x- and y-intercepts and graph 2x + 4y = 12 15. Write the equation of the line in point-slope form with slope m = -3, passing through point (2, -1). 16. Graph y = |x| + 1 17. Graph y = |x + 1|

18. The height (h) in inches of a tree is given by h = 2m + 7 where m = months. What is the y-intercept

and what does it represent? 19. A club sold hamburgers (x) for $3 and hot dogs (y) for $2.50. They raised $240. Write an equation

to find out how many of each item was sold. What are three combinations of hamburgers and hot dogs the club can buy for $240? Graph, label each axis appropriately, and indicate each intercept.

20. Is each of the following a linear function? Explain. a. x3 + y = 7 b. x = 3y – 9 c. y = |x – 7| d. 11x + 3y = 6 21. Find the equation of the line that passes through the points (3, 5) and (6, 13). Write your equation in

slope intercept form. State the slope and y-intercept.

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