Question

Find the equation for the linear function that passes through the points ( see photo )

Answer 1

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

Explanation:

step 1

Find the slope m

we have

(-2,-5) and (4,4)

The slope is equal to

`m=(4+5)/(4+2)`

`m=(9)/(6)`

simplify

`m=(3)/(2)`

step 2

Find the equation of the line into slope point form

`y-y1=m(x-x1)`

we have

`m=(3)/(2)`

`(4,4)`

substitute

`y-4=(3)/(2)(x-4)`

step 3

Convert to slope intercept form

`y-4=(3)/(2)(x-4)`

`y=(3)/(2)x-6+4`

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

Convert to function notation

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