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

1 Answer
Bill Jorgensen
May 21, 2018

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]}

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