Question

How do you write an equation through point (6, -8), perpendicular to y= -6x - 9?

Answer 1

`x-6y=42`

Explanation:

`y=color(blue)(-6)x-9` is an equation in slope-intercept form with a slope of `color(blue)(""(-6))`.

Any line perpendicular to it must have a slope of `-1/color(blue)(-6)=color(magenta)(1/6)`

If the required perpendicular line passes through `(color(red)6,color(brown)(-8))`
then, in slope-point form, its equation can be written as
`y-(color(brown)-8)=color(magenta)(1/6)(x-color(red)(6))`

Simplifying
`6(y+8)=x-6`

`6y+48=x-6`

`x-6y=42`