Question

An equation of a line perpendicular to the line represented by the equation `y=-1/2x - 5` and passes through `(6,-4)` is what?

Answer 1

`y-6 = 2(x+4)`

Explanation:

First find the slope `m` for the new line, rule for a perpendicular slope is:

your equation is in slope intercept form `y=mx+b`:

`y=-1/2x - 5`

`m'=-1/m`

`m=-1/2` so your new slope `m'=-1/(-1/2) = 2`

Now just use the slope point formula to solve your new line:

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

your point `(x_1,y_1) = (6, -4)`

`y-6 = 2(x-(-4))`

`y-6 = 2(x+4)`

you can do the algebra and convert this to standard form `Ax + By = C` or slope intercept for `y=mx+b` but the problem just asks for "an equation" so I assume this one would do fine.

here is the original graph:

graph{y=-1/2x - 5 [-18.92, 21.08, -14.56, 5.44]}

and here is the new one:

graph{y-6 = 2(x+4) [-41.75, 38.25, -17.36, 22.64]}