# How do you find the slope that is perpendicular to the line 2x+3y=7?

Jul 8, 2017

$\frac{3}{2}$

#### Explanation:

Rearrange the equation into the form y=mx+c where m is the gradient and c is the y intercept.

$y = - \frac{2}{3} x + 7$

The slope that is perpendicular to that line has a gradient with the negative reciprocal i.e. change the sign from minus to plus (or vice versa) and then flip it upside down.

$- \frac{2}{3}$ becomes $\frac{3}{2}$

You need a little more information to find the resulting equation i.e. a point which the line goes through where you will reuse the equation above (y=mx+c) to find the new y intercept.

Jul 8, 2017

See a solution process below:

#### Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

$\textcolor{red}{2} x + \textcolor{b l u e}{3} y = \textcolor{g r e e n}{7}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}}$

Let's call the slope of a perpendicular line: ${m}_{p}$

The formula for this slope is the inverse negative of the slope of the other line, or:

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

Therefore:

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