# What is the slope of any line perpendicular to the line passing through (-20,32) and (1,5)?

Dec 31, 2015

$\frac{7}{9}$

#### Explanation:

Given two lines with slopes ${m}_{1}$ and ${m}_{2}$, we say the lines are perpendicular if ${m}_{1} {m}_{2} = - 1$. Note that this implies ${m}_{2} = - \frac{1}{m} _ 1$.

Then, to find the slope ${m}_{2}$ of a line perpendicular to the line passing through $\left(- 20 , 32\right)$ and $\left(1 , 5\right)$ all we need to do is find the slope ${m}_{1}$ of the given line and apply the above formula.

The slope of a line passing through points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by $\text{slope" = "increase in y"/"increase in x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

So
${m}_{1} = \frac{5 - 32}{1 - \left(- 20\right)} = \frac{- 27}{21} = - \frac{9}{7}$

Applying ${m}_{2} = - \frac{1}{m} _ 1$ this means the slope ${m}_{2}$ of a line perpendicular to that line will be

${m}_{2} = - \frac{1}{- \frac{9}{7}} = \frac{7}{9}$