# How do you find the slope that is perpendicular to the line (4, 19) and (-3, 5)?

Mar 18, 2018

The slope of the line which is perpendicular to the line (4, 19); (-3, 5) is $- \frac{1}{2}$

#### Explanation:

Given -

(4, 19); (-3, 5)

The slope of the given line

${x}_{1} = 4$
${y}_{1} = 19$
${x}_{2} = - 3$
${y}_{2} = 5$

${m}_{1} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{5 - 19}{- 3 - 4} = \frac{- 14}{- 7} = 2$

The slope of the line which is perpendicular to a given line

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

The slope of the line which is perpendicular to the line (4, 19); (-3, 5) is $- \frac{1}{2}$