To find the rate of change of height off the ground with respect to the number of steps, we need to determine the slope between any two points in the table. The slope formula is:

$\text{slope} = \frac{\text{change in height}}{\text{change in number of steps}}$

Let's use the first two points in the table:
(3 steps, 21 inches) and (5 steps, 35 inches).

The change in height is:
$35 - 21 = 14 \text{ inches}$

The change in the number of steps is:
$5 - 3 = 2 \text{ steps}$

Now, calculate the slope:
$\frac{14 \text{ inches}}{2 \text{ steps}} = 7 \text{ inches per step}$

Thus, the rate of change of height with respect to the number of steps is 7 inches per step. The correct answer is option C (7 in. per step).

Would you like any further explanation or details on this problem?

Here are 5 related questions to expand on this topic:

1. How do we interpret the slope in the context of a linear relationship?
2. How can you find the slope using any other two points from the table?
3. What is the equation of the line that describes this relationship between steps and height?
4. How would you calculate the height for 15 steps using the slope?
5. How can you determine if the relationship between steps and height is truly linear?

Tip: When dealing with linear relationships, the slope is constant, meaning the rate of change remains the same across all intervals.