What is the slope of any line perpendicular to the line passing through (-3,1) and (-6,12)?

Apr 27, 2018

$\frac{3}{11}$

Explanation:

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 $\frac{3}{11}$