Question

What is the equation of the line perpendicular to `y=-2/15x` that passes through `(-4,24)`?

Answer 1

`y=15/2x+54` or `y=7.5x+54`

Explanation:

The line `y=-2/15x` has a slope of `m=-2/15`

The perpendicular slope of `m = -1/m`

Therefore the perpendicular line would have a slope of `m=15/2`

The point-slope equation of a line is

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

The perpendicular line passes through `(-4,24)`

`y-24=15/2(x-(-4))`

`y-24=15/2x+30`

`y=cancel(-24)cancel(+24)=15/2x+30+24`

`y=15/2x+54` or `y=7.5x+54`