# What is the slope of any line perpendicular to the line passing through (-2,7) and (-2,3)?

Nov 9, 2017

$y = 0$ graph{y=0x [-9.83, 10.17, -4.96, 5.04]}

#### Explanation:

I'll be using slope-intercept form, $y = m x + b$, for this.

A perpendicular line is a line with a slope that is both the inverse and the reciprocal of the original slope. For example, $y = \frac{2}{3}$ is perpendicular to $y = \left(- \frac{3}{2}\right)$. It does not matter what the y-intercept $b$ is in this situation, the slope is what's important.

To find the slope, use the rise-over-run formula of $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{3 - 7}{\left(- 2\right) - \left(- 2\right)} \Rightarrow \frac{- 4}{0}$

This will be a special case. Since dividing by 0 is undefined, this makes your slope undefined. Contrary to the rules explained above, which should work for all other questions, your slope in this case is a perfectly horizontal line, as undefined is perfectly vertical.

A horizontal line is called a slope of zero. As you'll see, the name is quite fitting, because your answer is:

$y = 0$