What is the slope of any line perpendicular to the line passing through (-4,1) and (-3,7)?

Mar 31, 2018

The slope of any line perpendicular to given line is $\left(- \frac{1}{6}\right)$

Explanation:

We know that,

$\left(1\right)$ Slope of the line passing through $A \left({x}_{1} , {y}_{1}\right) \mathmr{and} B \left({x}_{2} , {y}_{2}\right)$ is

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

$\left(2\right)$ If the slope of the line ${l}_{1}$ is ${m}_{1} \mathmr{and}$ the slope of
the line
${l}_{2}$ is ${m}_{2}$ then

${l}_{1} \bot {l}_{2} \iff {m}_{1} {m}_{2} = - 1$

We have line ${l}_{1}$ passing through $A \left(- 4 , 1\right) \mathmr{and} B \left(- 3 , 7\right)$.

Using $\left(1\right)$ we get

${m}_{1} = \frac{7 - 1}{- 3 + 4} = 6$

Now from $\left(2\right)$,we have

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

$\implies \left(6\right) {m}_{2} = - 1$

$\implies {m}_{2} = - \frac{1}{6}$

$\therefore$The slope of any line perpendicular to given line is $\left(- \frac{1}{6}\right)$