Question

Answer has to be in slope intercept form

Answer 1

Given:

Perpendicular line:

`$m(r)=-(2)/(3) r-3`

`f(-2)=-9`

To find:

The equation of the linear function f.

Solution:

`$m(r)=-(2)/(3) r-3`

Slope of line m is =
`-(2)/(3)`

If two lines are perpendicular then the slope of one equation is negative reciprocal of the other.

Slope of line f =
`(3)/(2)`

`f(-2)=-9`

This means f has point (-2, -9).

Using point-slope formula:

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

Here
`x_1=-2, y_1=-9` and
`m=(3)/(2)`

`$y-(-9)=(3)/(2) (x-(-2))`

`$y+9=(3)/(2) (x+2)`

`$y+9=(3)/(2) x+(3)/(2) \cdot 2`

`$y+9=(3)/(2) x+3`

Subtract 9 from both sides.

`$y+9-9=(3)/(2) x+3-9`

`$y=(3)/(2) x-6`

Substitute x = r and y = f.

`$f(r)=(3)/(2) r-6`

The linear equation is
`f(r)=(3)/(2) r-6`.