AnswersLA-Algebra II AEquations in One Variable

Rate of Change Answers

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Maria created a graph of B(t), the temperature over time. For the interval between t = 3 and t = 7, the average rate of change in her graph of B(t) is 8. Which statement must be true?

A
The temperature was 8 degrees higher when t = 7 than when t = 3.
B
The temperature was 8 times higher when t = 7 than when t = 3.
C
The temperature was 32 degrees higher when t = 7 than when t = 3.
D
The temperature was 2 degrees higher when t = 7 than when t = 3.
2
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If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

A
10
B
40
C
100
D
198
3

If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?

A
y = one-ninth
Option A
B
y = two-thirds
Option B
C
54
D
96
4

Which relation is a direct variation that contains the ordered pair (2, 7)?

A
y = 4x – 1
B
y = StartFraction 7 Over x EndFraction
Option B
C
y = two-sevenths x
Option C
D
y = seven-halves x
Option D
5

The cost of soup, s, varies directly with the number of cans, c. When c is 4, the cost is $3. Which graph represents the cost of the soup?

A
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A curve opens up to the right and approaches the x-axis and the y-axis. The vertex is around (1, 1).
Option A
B
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A straight line has a positive slope and goes through (0, 0), (3, 4), and (6, 8).
Option B
C
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A straight line has a positive slope and goes through (0, 0), (4, 3), and (8, 6).
Option C
D
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A curve starts at (0, 0) and opens up to the left. The curve goes through (4, 3) and (5, 6).
Option D
6

The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and 8 seconds.

Question illustration
A
0.5 meters per second
B
0.8 meters per second
C
2 meters per second
D
3 meters per second
7

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