Question

How do you write an equation of a line passing through (6, 3), perpendicular to `y = 2x + 2`?

Answer 1

`x+2y=12`

Explanation:

`y=color(green)(2)x+2` is an equation in slope-intercept form with a slope of `color(green)(m=2)`

All lines perpendicular to `y=color(green)(2)x+2` will have a slope
`color(white)("XXX")-1/color(green)(m)=color(red)(-1/2)`

If a line has a slope of `color(red)(""(-1/2))` and passes through `color(blue)(""(6,3))`
then we can write its equation in slope-point form as
`color(white)("XXX")y-color(blue)(3)=color(red)(""(-1/2))(x-color(blue)(6))`

While this is a valid answer, we would normally rearrange it into a simpler form:
`color(white)("XXX")2y-6=6-x`
or
`color(white)("XXX")x+2y=12`