Two linear functions of x are shown. which statement about the functions is true?

Option D. The rate of change of function 2 is less than the rate of change of the function 1

Step-by-step explanation:

step 1

Find the rate of change and the y-intercept of the function 1

we have

This is the equation of the line in slope intercept form

where

the slope is m=30

the y-intercept is b=19

Remember that the slope is the same that the rate of change

so

The rate of change of the function 1 is

The y-intercept of the function 1 is

step 2

Find the slope of the function 2

From the data in the table take two points

(-12,-311) and (1,14)

The formula to calculate the slope between two points is equal to

substitute the values

step 3

Find the equation of the function 2 in slope intercept form

we have

substitute

solve for b

The equation of the function 2 is

so

The rate of change of the function 2 is

The y-intercept of the function 2 is

Verify each statement

case A) Function 2 can be described by the equation y=25x-100

The statement is false

Because the equation of the function 2 is

case B) Function 2 can be described by the equation y=13x-11

The statement is false

Because the equation of the function 2 is

case C) The y-intercept of function 1 is less than the y-intercept of the function 2

The statement is false

Because, the y-intercept of function 1 is greater than the y-intercept of the function 2

case D) The rate of change of function 2 is less than the rate of change of the function 1

The statement is true

the bottom of the spinner is not flat.

step-by-step explanation: