# What is the slope of any line perpendicular to the line passing through (8,-6) and (-7,1)?

Dec 8, 2015

For a line to be perpendicular to a given line their slopes have to multiply to give a result of $- 1$

#### Explanation:

So we first get the slope of the line:
(btw: $\Delta$ means difference)

${m}_{1} = \frac{\Delta y}{\Delta x} = \frac{1 - \left(- 6\right)}{- 7 - 8} = \frac{7}{-} 15 = - \frac{7}{15}$

Now the perpendicular line will have a slope of:

${m}_{2} = + \frac{15}{7}$ because $\left(- \frac{7}{15}\right) \cdot \left(+ \frac{15}{7}\right) = - 1$