Question

1. Which answer is the equation of the line represented in function notation?

2.Given graph for function f (x) given above,find the f (-2). f (-2) =

Answer 1

Part 1)
`f(x)=-(2/3)x-2`

Part 2)
`f(-2)=-2/3`

Explanation:

step 1

Find the equation of the line

Let

`A(-3,0), B(0,-2)`

The equation of the line into slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem

The point B is the y-intercept

so

b=-2

Find the slope m

`m=(-2-0)/(0+3)=-2/3`

substitute

`y=-(2/3)x-2`

In function notation

`f(x)=-(2/3)x-2`

step 2

Find f(-2)

substitute the value of x=-2 in the function

`f(-2)=-(2/3)(-2)-2=(4/3)-2=-2/3`