Question

Consider the two functions described below.

Function 1 is represented by the graph below. It shows the distance Carl travels y in x hours at a constant speed.

Function 2 represents the following scenario: The equation y = 25x gives the distance y Sheila travels in x hours.

Which is a correct description of how to compare the rates of change in each scenario?
A. Compare the change in x over the change in y for each function.
B. Compare the change in y over the change in x for each function.
C. Compare the values at which the graphs cross the x-axis.
D. Compare the values at which the graphs cross the y-axis.

Answer 1

B. Compare the change in y over the change in x for each function.

Explanation:

Find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

Change in y\Change in x

`(200)/(5) = 40`

y = 40x

By the definition of slope, you have your answer.

I am joyous to assist you anytime.

Answer 2

The correct option is B) Compare the change in y over the change in x for each function.

Explanation:

Consider the provided information.

We need to determine the correct description how to compare the rates of change in each scenario.

The rate of change of a function is:
`(Rise)/(Run)`

Or the rate of change of a function is change in y over the change in x.

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

To compare the rates of change we need to compare the change in y over the change in x for each function.

Hence, the correct option is B) Compare the change in y over the change in x for each function.