Question

The equation represents Function A, and the graph represents Function B:

Function A: f(x) = x − 9

Which equation best compares the slopes of the two functions?

A.) Slope of Function B = 2 x Slope of Function A
B.) Slope of Function A = Slope of Function B
C.) Slope of Function A = 2 x Slope of Function B
D.) Slope of Function B = − Slope of Function A

Answer 1

The correct option is A.

Explanation:

The slope intercept form of a line is

`y=mx+b` .... (1)

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

The equation of Function A is

`f(x)=x-9` .... (2)

From (1) and (2) we get

`m=1`

It means slope of Function A is 1.

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then slope of the line is

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

From the given graph it is clear that the line passes through two points (0,-1) and (1,1).

`m=(1-(-1))/(1-0)=2`

The slope of Function B is 2.

We can say that

Slope of Function B = 2 x Slope of Function A

Therefore the correct option is A.

Answer 2

A.) Slope of function B = 2 * the slope of Function A.

Explanation:

The slope of Function A is 1 ( because of the x ( = 1x) in the equation).

From the graph, the slope of Function B = 5 / 2.5 = 2.