# Find the slope of any line perpendicular to the line passing through (−3,1) and (−6,12)

Find the slope of any line perpendicular to the line passing through (−3,1) and (−6,12)
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Gwendolyn Alexander
First, let's find the slope through the given two points: $\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$, where there are two points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$:
$\frac{12-1}{-6-\left(-3\right)}$
$\frac{11}{-3}$
$-\frac{11}{3}$
Perpendicular slopes are opposite reciprocals of one another:
Opposites: put a negative sign in front of a positive number or take away a negative sign from a negative number (ex. $-3,3$, $\frac{7}{11},-\frac{7}{11}$
Reciprocals: flip the numerator and denominator (ex. $\frac{12}{5},\frac{5}{12}$, $4,\frac{1}{4}$)
The opposite of $-\frac{11}{3}$ is $\frac{11}{3}$
The reciprocal of $\frac{11}{3}$ is $\frac{3}{11}$