# What is the slope of a line perpendicular to the graph of the equation 5x - 3y =2?

May 27, 2018

$- \frac{3}{5}$

#### Explanation:

Given: $5 x - 3 y = 2$.

First we convert the equation in the form of $y = m x + b$.

$\therefore - 3 y = 2 - 5 x$

$y = - \frac{2}{3} + \frac{5}{3} x$

$y = \frac{5}{3} x - \frac{2}{3}$

The product of the slopes from a pair of perpendicular lines is given by ${m}_{1} \cdot {m}_{2} = - 1$, where ${m}_{1}$ and ${m}_{2}$ are the lines' slopes.

Here, ${m}_{1} = \frac{5}{3}$, and so:

${m}_{2} = - 1 \div \frac{5}{3}$

$= - \frac{3}{5}$

So, the perpendicular line's slope will be $- \frac{3}{5}$.

May 27, 2018

The slope of a line perpendicular to the graph of the given equation is $- \frac{3}{5}$.

#### Explanation:

Given:

$5 x - 3 y = 2$

This is a linear equation in standard form. To determine the slope, convert the equation into slope-intercept form:

$y = m x + b$,

where $m$ is the slope, and $b$ is the y-intercept.

To convert the standard form to slope-intercept form, solve the standard form for $y$.

$5 x - 3 y = 2$

Subtract $5 x$ from both sides.

$- 3 y = - 5 x + 2$

Divide both sides by $- 3$.

$y = \frac{- 5}{- 3} x - \frac{2}{3}$

$y = \frac{5}{3} x - \frac{2}{3}$

The slope is $\frac{5}{3}$.

The slope of a line perpendicular to the line with slope $\frac{5}{3}$ is the negative reciprocal of the given slope, which is $- \frac{3}{5}$.

The product of the slope of one line and the slope of a perpendicular line equals $- 1$, or ${m}_{1} {m}_{2} = - 1$, where ${m}_{1}$ is the original slope and ${m}_{2}$ is the perpendicular slope.

$\frac{5}{3} \times \left(- \frac{3}{5}\right) = - \frac{15}{15} = - 1$

graph{(5x-3y-2)(y+3/5x)=0 [-10, 10, -5, 5]}