# How do you find the slope and intercept of 3x-2y=9?

Mar 15, 2018

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

$\textcolor{red}{3} x + \left(\textcolor{b l u e}{- 2}\right) y = \textcolor{g r e e n}{9}$

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

Substituting gives:

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

The $y$-intercept of an equation in standard form is: $\frac{\textcolor{g r e e n}{C}}{\textcolor{b l u e}{B}}$

Substituting gives:

$\frac{\textcolor{g r e e n}{9}}{\textcolor{b l u e}{- 2}} = - \frac{9}{2}$ or $\left(0 , - \frac{9}{2}\right)$