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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change of height off the ground with respect to the number of steps, we need to calculate the slope of the linear relationship between the two variables.

Let's consider the given table:
Number of Steps (x): 1, 2, 3, 4, ...
Height off the Ground (y): 10, 20, 30, 40, ...

To find the slope, we can choose any two points on the table and use the formula:

Slope = (Change in y)/(Change in x)

Let's choose two points: (1, 10) and (2, 20)

Change in y = 20 - 10 = 10
Change in x = 2 - 1 = 1

Slope = (Change in y)/(Change in x) = 10/1 = 10

Therefore, the rate of change of height off the ground with respect to the number of steps is 10 inches per step.