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
A: yes; y = 5x
B: yes; y = 10x
C: yes; y = 1.625x
D: no; y does not vary directly with x
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
A: yes; y = 2x
B: yes; y = 0.5x
C: yes; y = 1.5x
D: no; y does not vary directly with x.
5. The table shows the number of miles driven over time.
Time (hours) Distance (miles)
4 204
6 306
8 408
10 510
Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relationship.
A: 51/1; your car travels 51 miles every 1 hour.
B: 204; your car travels 204 miles.
C: 1/51; your car travels 51 miles every 1 hour.
D: 10; your car travels for 10 hours.
7. What is the slope of the line that passed through the pair of points (1, 7) and (10, 1)?
A: 3/2
B: -2/3
C: -3/2
D: 2/3
9: Write an equation in point-slope form for the line through the given point with the given slope.
(8, 3); m = 6
A: y + 3 = 6 (x - 8)
B: y - 3 = 6 (x - 8)
C: y - 3 = 6 (x + 8)
D: y + 3 = 6x + 8
10. Write an equation in point-slope form for the line through the given point with the given slope.
(-10, -6); m = -5/8
A: y - 6 = -5/8 (x - 10)
B: y - 6 = -5/8 (x + 10)
C: y + 6 = -5/8 (x + 10)
D: y + 10 = -5/8 (x + 6)
11. The table shows the height of a plant as i 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
A: y - 21 = 7/5 (x - 3)
B: y - 21 = 7 (x - 3)
C: y - 3 = 7/2 (x - 21)
D: The relationship is nonlinear.
13. Write y = -2/3x + 7 in standard form using integers.
A: 2x + 3y = 21
B: 3x - 2y = 21
C: -2x - 3y = 21
D: -2x + 3y = 7
14. Write an equation for the line that is parallel to the given line and passes through the given point.
y = 3x + 7; (2, 10)
A: y =
B: y = 3x + 4
C: y = -3x + 4
D: y = (-1/3)x + 4
15. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = -4x + 3
-2x + 8y = 5
A: Parallel
B: Perpendicular
C: Neither
16. Tell whether the lines for each pair of equations are parallel, perpendicular or neither.
y = -1/4x + 10
-2x + 8y = 6
A: Parallel
B: Perpendicular
C: Neither
17. Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y - 3 = 8/3(x + 2); (-2, 3)
A: y + 3 = -3/8(x - 2)
B: y - 3 = -3/8(x + 2)
C: y - 2 = -3/8(x + 3)
D: y + 3 = 3/8(x - 2)
19. Describe how the graphs of y = |x| and y = |x + 2| are related.
A: The two graphs have the same shape but the second graph is shifted 2 units right.
B: The two graphs have the same shape but the second graph is shifted 2 units up.
C: The two graphs have the same shape but the second graph is shifted 2 units left.
D: The two graphs have the same shape but the second graph is shifted 2 units down.
(Please leave a summary of the answers and questions at the bottom of the response, for example, 1. B, 2. C, and etcetera. Thank you.)
1. C
2. D
5. A
7. C
9. A
10. A
11. A
13. D
14. A
15. C
16. C
17. B
19. A
Summary:
1. C, 2. D, 5. A, 7. C, 9. A, 10. A, 11. A, 13. D, 14. A, 15. C, 16. C, 17. B, 19. A.