Question

This table shows input and output values for a linear function f(x).

What is the difference of outputs for any two inputs that are one value apart?

x f(x)
---------------------
-3 -57.6
----------------------
-2 -36.4
----------------------
-1 -15.2
----------------------
0 6
----------------------
1 27.2
----------------------
2 48.4


A) -5
B) 1
C) 21.2
D) 27.2

Answer 1

C

Explanation:

This question asks us to find the difference in output or y values or consecutive x-values (values 1 unit away from each other). This is just a rate of change or slope. We will use the slope formula:

Slope:
`m=(y_2-y_1)/(x_2-x_1)`

We substitute
`x_1=-3\\y_1=-57.6` and
`x_2=-2\\y_2=-36.4`

`m=(-36.4-(-57.6))/(-2-(-3))`

`m=(-36.4+57.6)/(-2+3)=(21.2)/(1) =21.2`

Answer C.