What is the slope of a line perpendicular to the line whose equation is x+ 2y = 2

Answer 1

The slope of the normal (perpendicular) is 2, the negative reciprocal of -1/2.

Answer 2

Hi Hillary!

First you need to find the slope of the line x+2y=2. The first way to do this is by converting the equation of the line to slope intercept form (y=mx+b).

x + 2y = 2 (subtract x from both sides)

-x -x

2y = -x + 2 (divide both sides by 2)

y = -x/2 + 2/2 (simplify)

y = -1/2 x + 1

Thus, the number in front of the x is your slope. Here the slope is -1/2.

The other way to find the slope is to use -A/B. Anytime your equation is in standard form (Ax + By = C), you can use this shortcut to find the slope. Since A = 1 and B = 2, - A/B = -1/2.

Now that we know the slope of the line (-1/2) we need to find the opposite reciprocal. Remember the reciprocal means to flip the fraction and opposite means switch the sign. So our perpendicular slope is 2/1 or just 2.

I hope this helps. Good luck!

Here's a Khan Academy video (https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/perpendicular-lines).