Linear Functions Unit Test

Multiple Choice

1. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

x y
8 13
16 26
24 39

2. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

x y
40 32
28 16
16 12

3. Match the equation with its graph.

- x - y =

4. Match the equation with its graph.

-0.4x - 0.8y = 0.10

5. The table shows the number of miles driven over time.
Time (hours)    Distance (miles)
4                          184
6                          276
8                          368
10                        460

Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relationship.

6. Find the slope of the line.

7. What is the slope of the line that passes through the pair of points (1, 7) and (10, 1)?

8. What is the slope of the line that passes through the pair of points (- , -3) and (-5, )?

9. What is the slope of the line?

10. Write an equation in point-slope form for the line through the given point with the given slope.

(8, 3); m = 5

11. Write an equation in point-slope form for the line through the given point with the given slope.

(-10, -6); m =

12. The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant's height at any time?

Time (months)       Plant Height (cm)
3                                   21
5                                   35
7                                   49
9                                   63

13. What is the graph of the equation?

x = -3

14. Write y = - x + 7 in standard form using integers.

15. Write an equation for the line that is parallel to the given line and passes through the given point.

y = 5x + 10; (2, 14)

16. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

y = -3x + 7

-2x + 6y = 3

17. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

y = ( )x + 8

-2x + 8y = 4

18. Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y - 2 = (x + 5); (-4, 9)

19. Below are the functions of y = |x| and y = |x| - 5. How are the functions related?

20. Describe how the graphs of y = |x| and y = |x + 5| are related.

21. Graph y = |x| - 2.

22. Graph y = |x - 4|.

23. Which type of correlation is suggested by the scatter plot?

Short Answer

24. You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.015. How confident can you be that your predicted value will be reasonably close to the actual value?

25. A college football coach wants to know if there is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. He sets up the following test and records the data:

Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The table shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?

Round any values to the nearest tenth, if necessary.

Leg Press (reps) 15 18 8 30 26 12 21

40-yard Dash (s) 5.2 6.3 6.8 8.2 8.0 5.3 5.9