Question

A construction worker built steps up to a home. The table shows the linear relationship between the height off the ground in inches and the number of steps.

What is the rate of change of height off the ground with respect to the number of steps
number of steps
3
5
7
9
11
height (inches)
20
36
52
68
84

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change of the height off the ground with respect to the number of steps, we need to calculate the difference in height for each pair of consecutive steps and divide it by the difference in the number of steps.

Let's calculate the difference in height and the difference in the number of steps for each pair of consecutive steps:

Difference in height (inches):
36 - 20 = 16
52 - 36 = 16
68 - 52 = 16
84 - 68 = 16

Difference in number of steps:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
11 - 9 = 2

Now, let's find the rate of change by dividing the difference in height by the difference in number of steps for each pair:

rate of change = difference in height / difference in number of steps

For the first pair:
rate of change = 16 / 2 = 8 inches/steps

For the second pair:
rate of change = 16 / 2 = 8 inches/steps

For the third pair:
rate of change = 16 / 2 = 8 inches/steps

For the fourth pair:
rate of change = 16 / 2 = 8 inches/steps

Therefore, the rate of change of height off the ground with respect to the number of steps is 8 inches/steps.