Question

The graph shows the height of an airplane as it descends to land

Answer 1

ANSWER and EXPLANATION

a) Yes, the function has a constant rate of change.

Rate of change of a function is the change in y values divided by the change in x values. In other words, the change in the output of the function over the change in the input.

To find the rate of change, we use the formula:

`(y_2-y_1)/(x_2-x_1)`

We need to pick two points (x1, y1) and (x2, y2).

Let us pick (1,7000) and (3, 1000)

Therefore, the rate of change is:

`\begin{gathered} \frac{1000\text{ - 7000}}{3\text{ - 1}} \\ =\text{ }(-6000)/(2) \\ =\text{ -3000 ft/min} \end{gathered}`

Therefore, the rate of change is -3000 ft/min.

b) The slope of the line is the same as the rate of change, so the slope is -3000 ft/min.

c) The slope and the rate of change are two ways of defining the same concept.

They both tend to measure the change in the output values of a function with respect to the change in the input values.

d) This has the same answer as option C.