# What is the slope of a line parallel and perpendicular to 6x + 4y = -4?

Apr 26, 2017

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

A line parallel to this line will have the same slope as:

$\textcolor{red}{6} x + \textcolor{b l u e}{4} y = \textcolor{g r e e n}{- 4}$

$m = - \frac{\textcolor{red}{6}}{\textcolor{b l u e}{4}} = - \frac{3}{2}$

Let us call the slope of the perpendicular line ${m}_{p}$.

The formula for the slope of a perpendicular line is:

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

Substituting gives the slope of the perpendicular line as:

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