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 28
16 56
20 70
(1 point)
yes; y = 5x
yes; y = x + 20
yes; y = 3.5x
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
32 24
16 8
8 6
(1 point)
yes; y = 0.5x
yes; y = 2x
yes; y = 1.5x
no; y does not vary directly with x.
3. Match the equation with its graph.
– x – y =
(1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
4. A right triangle has a leg b of length 5 and a hypotenuse of length 15. What is the length of the other leg,
a? Round to the nearest tenth, if necessary.
(1 point)
10.0
15.8
14.1
3.2
5. The table shows the number of miles driven over time.
Express the relationship between distance and time in simplified form as a unit rate. Determine which
statement correctly interprets this relationship.
(1 point)
; your car travels 51 miles every 1 hour.
204; your car travels 204 miles.
; your car travels 51 miles every 1 hour.
10; your car travels for 10 hours.
6. Find the slope of the line. (1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
–4
4
7. Which of the following lengths of lines could be used to create a right triangle? (1 point)
7, 8, 11
6, 8, 10
4, 9, 15.3
2, 7, 9
8. Find the length of a line segment with endpoint C at (–5, 2) and endpoint D at (3, 7). Round your
answer to the nearest tenth, if necessary.
(1 point)
3.6
5.4
9.4
11.7
9. What is the slope of the line that passes through the pair of points? (3, –1), and (5, –8)? (1 point)

10. What is the slope of the line? (1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
0
1
Infinity
Undefined
11. Write an equation in point-slope form for the line through the given point with the given slope.
(5, 2); m = 3
(1 point)
y + 2 = 3(x – 5)
y + 2 = 3x – 5
y – 2 = 3(x + 5)
y – 2 = 3(x – 5)
12. Find the midpoint of a segment with point D at (–8, 2) and point E at (4, –2). (1 point)
(–2, 0)
(–6, 2)
(–6, –2)
(–3, –1)
13. Which type of correlation is suggested by the scatter plot? (1 point)
positive correlation
negative correlation
equal correlation
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
no correlation
14. 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)
2 16
4 32
6 48
8 64
(1 point)
y – 16 = 8(x – 2)
y – 16 = 8x – 2
y + 16 = 8(x + 2)
The relationship is nonlinear.
15. What is the graph of the equation?
x = –5
(1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
16. Write y = – x + 7 in standard form using integers.
(1 point)
2x + 3y = 21
3x – 2y = 21
–2x – 3y = 21
–2x + 3y = 7
17. Write an equation for the line that is parallel to the given line and passes through the given point.
y = 5x + 10; (2, 14)
(1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
y = x + 4
y = 5x + 4
y = – x – 4
y = 5x – 68
18. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –4x + 3
–2x + 8y = 5
(1 point)
parallel
perpendicular
neither
19. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = ( )x + 8
–2x + 8y = 4
(1 point)
parallel
perpendicular
neither
20. 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)
(1 point)
y – 9 = (x – 4)
y – 9 = (x – 4)
y – 9 = (x + 4)
y – 9 = (x + 4)
21. Below are the functions of y = |x| and y = |x| – 9. How are the functions related? (1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEXV��� ����
The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 9.
The functions have the same y-intercept. The second function is steeper than y = |x|.
The two functions are the same.
The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –9.
22. Graph y = |x+3|. (1 point)
�������� /LQHDU )XQFWLRQV 8QLW 7HVW
KWWSV���ZZZ�FRQQH[XV�FRP�DVVHVVPHQWV�HQJLQH�DVS["UHVL]H WUXH SULQWSUHYLHZ WUXH FORVH WUXH SRSXS WUXH LG$VVHVVPHQW ������ VHOI 7UXH LG:HEX��� �����
23. Graph y = |x| + 4. (1 point)

1. c

2. b
3. a

I'm sorry, but as an AI text-based bot, I cannot create or display graphs.

To determine if y varies directly with x, we need to see if the ratio y/x is constant for each pair of values.

For the first data table:
x y
8 28
16 56
20 70

Let's check if the ratio y/x is constant:
28/8 = 3.5
56/16 = 3.5
70/20 = 3.5

Since the ratio y/x is constant (3.5), we can conclude that y varies directly with x.
The equation for the direct variation is y = 3.5x.

For the second data table:
x y
32 24
16 8
8 6

Let's check if the ratio y/x is constant:
24/32 = 0.75
8/16 = 0.5
6/8 = 0.75

Since the ratio y/x is not constant, we can conclude that y does not vary directly with x.

Now let's move on to the next question.

1. Yes, Y = 3.5x.

2. No.

4. a^2 + b^2 = c^2.
b = 5, c = 15, a = ?.

5. 51 * T = 204.

8. (-5,2), (3,7).
L^2 = (3+5)^2 + (7-2)^2 = 89,
L = 9.4.

9. (3,-1), (5,-8).
m = (-8+1)/(5-3) =

11. (5,2), (x,y), m = 3.
m = (y-2)/(x-5) = 3,
y-2 = 3(x-5).

12. (-8,2), (x,y), (4,-2).
x+8 = 1/2(4+8) = 6, X = -2.

y-2 = 1/2(-2-2) = -2, Y = 0.

15. X = -5 is a vertical line.