Question

Find the equation of a line with the given information:

f(- 6) = 8 and f( - 8) = – 1.
Wrote answer in point slope form

Answer 1

`y -8= (9)/(2)(x +6)`

Explanation:

Given

`f(-6) = 8`

`f(-8) = -2`

Required

Determine the equation in point-slope form

The general function notation is:

`f(x) = y`

So, in
`f(-6) = 8`

`(x_1,y_1) = (-6,8)`

`f(-8) = -1`

`(x_2,y_2) = (-8,-1)`

Calculate the slope (m)

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

`m = (-1-8)/(-8-(-6))`

`m = (-1-8)/(-8+6)`

`m = (-9)/(-2)`

`m = (9)/(2)`

The equation is then calculated as:

`y -y_1= m(x-x_1)`

`y -8= (9)/(2)(x - (-6))`

`y -8= (9)/(2)(x +6)`