# What is the slope of any line perpendicular to the line passing through (5,-6) and (-2,1)?

Jul 4, 2016

Slope is 1.

#### Explanation:

The slope of the line is given by $m = \frac{\Delta y}{\Delta x}$

$m = \frac{1 - \left(- 6\right)}{\left(- 2\right) - 5} = \frac{7}{- 7} = - 1$

The product of two perpendicular gradients is always equal to -1, so

$m \cdot {m}_{p e r p} = - 1$

${m}_{p e r p} = \frac{- 1}{-} 1 = 1$