Question

The graph represents function 1, and the equation represents function 2:

A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 4.

Function 2
y = 8x + 12

How much more is the rate of change of function 2 than the rate of change of function 1?

3
4
5
8

Answer 1

The rate of change of function 1 (a horizontal line) is zero.

The rate of change (slope) of function 2 is the x-coefficient, 8.

8 is 8 more than 0.

The 4th selection is appropriat:
  8

Answer 2

Answer:

Option D.

Step-by-step explanation:

The slope of a horizontal line is 0.

It is given that the function 1 is a horizontal line that passing through the y-axis at y = 4.

It means the rate of change of function 1 is 0.

The slope intercept form of a linear function is

$y=mx+b$            .... (1)

where, m is slope and b is y-intercept.

The function 2 is

$y=8x+12$           .... (2)

On comparing (1) and (2), we get

$m=8$

The rate of change of function 2 is 8.

The difference between rate of change is

$8-0=8$

The rate of change of function 2 is 8 more than the rate of change of function 1.

Therefore, the correct option is D.