# What is the slope of a line perpendicular to this line? Y=3/4x

May 4, 2018

$- \frac{4}{3}$

#### Explanation:

Here

$y = m x$

is the given eq, with $m$ being the slope of the given line. Therefore, the slope of this line is $\frac{3}{4}$ $\left(m\right)$.

But the slope of the line perpendicular to the given line is $= - \frac{1}{m}$, so the answer is $= - \frac{1}{\frac{3}{4}}$

which is $= - \frac{4}{3}$.

May 4, 2018

The perpendicular slope is $- \frac{4}{3}$.

#### Explanation:

Given:

$y = \frac{3}{4} x$

The slope that is perpendicular to $\frac{3}{4}$ is its negative reciprocal, which is $- \frac{4}{3}$.

Mathematically

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

where ${m}_{1}$ is the given slope and ${m}_{2}$ is the perpendicular slope.

$\frac{3}{4} {m}_{2} = - 1$

Multiply both sides by $\frac{4}{3}$.

${\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}^{1} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}^{1} \times {\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}^{1} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}^{1} {m}_{2} = - 1 \times \frac{4}{3}$

Simplify.

${m}_{2} = - \frac{4}{3}$