# How do you find the slope of a line parallel to the graph of each equation 3x + 2y = 6?

Oct 5, 2017

See a solution process below:

#### Explanation:

The slope of a parallel line will have the same slope as the original line.

The equation in the problem 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: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

$\textcolor{red}{3} x + \textcolor{b l u e}{2} y = \textcolor{g r e e n}{6}$

The slope of this line is:

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

Therefore, the slope of a parallel line is $- \frac{3}{2}$