Question

A linear function f models a relationship in which the dependent variable decreases 4 units for every 2 units the independent variable increases. The

value of the function at 0 is -2
Identify the slope, y-intercept, and x-intercept of the graph

Answer 1

Answer:value of the function at 0 is -2

Explanation:

Answer 2

Part 1) The slope is
`m=-2`

Part 2) The y-intercept is the point (0,-2)

Part 3) The x-intercept is the point (-1,0)

Explanation:

step 1

Find the slope of the linear function

we know that

The dependent variable or output is the variable y

The independent variable or input is the variable x

we have that

The dependent variable decreases 4 units for every 2 units the independent variable increases

The slope m is

`m=(-4)/(2)=-(4)/(2)= -2`

step 2

Find the y-intercept

we have the point (0,-2)

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

The y-intercept is the point (0,-2)

step 3

Find out the equation of the linear function f in slope intercept form

`f(x)=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

we have

`m=-2`

`b=-2`

substitute

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

step 4

Find out the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

For f(x)=0

`0=-2x-2`

`2x=-2`

`x=-1`

The x-intercept is the point (-1,0)

see the attached figure to better understand the problem