# What is the slope of any line perpendicular to the line passing through (0,0) and (-1,1)?

May 11, 2018

$1$ is the slope of any line perpendicular to the line

#### Explanation:

The slope is rise over run, $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

The slope perpendicular to any line is it’s negative reciprocal. The slope of that line is negative one so the perpendicular to it would be $1$.

May 11, 2018

$y = - 1 x + 0$; the reciprocal is $y = 1 x + 0$

#### Explanation:

First, we need to find the slope of the line that passes through these two points, then, we can find its reciprocal (opposite, which is perpendicular). Here's the formula for finding a slope with two points:

$\frac{{Y}_{2} - {Y}_{1}}{{X}_{2} - {X}_{1}}$ = $m$, the slope

Label your ordered pairs:

(0, 0) $\left({X}_{1} , {Y}_{1}\right)$
(-1, 1) $\left({X}_{2} , {Y}_{2}\right)$

Now, plug-in your data:

$\frac{1 - 0}{- 1 - 0}$ = $m$

Simplify.

$\frac{1}{- 1}$ = $m$

m = $- 1$ , because 1 negative and 1 positive divide into a negative.

Now, let's find its equation by using the point-slope formula:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 0 = - 1 \left(x - 0\right)$

Distribute:

$y - 0 = - 1 x + 0$

Add zero to both sides:

$y = - 1 x + 0$

If $m$ = $\frac{1}{-} 1$, the negative reciprocal will be $\frac{1}{1}$, which makes $m$ change to 1.

Credit to Shantelle for correcting an error
https://www.mathsisfun.com/reciprocal.html
https://www.mathsisfun.com/definitions/reciprocal.html
http://www.purplemath.com/modules/strtlneq2.htm