# How do you find the slope and y-intercept for the graph of the equation: 9x - 3y = 81?

Dec 27, 2016

graph{y = 3x - 27 [-5, 10, -30, 5]}

The slope is $\textcolor{red}{3}$ and the y-intercept is $\textcolor{b l u e}{- 27}$ or ($\textcolor{b l u e}{0 , - 27}$)

#### Explanation:

To find the slope and y-intercept of this equation we must transform it into the slope-intercept form.

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and color(blue)(b is the y-intercept value.

We can solve this equation for $y$ to transform the equation we have been given in this problem into this form:

$9 x - 3 y = 81$

$9 x - \textcolor{red}{9 x} - 3 y = \textcolor{red}{- 9 x} + 81$

$0 - 3 y = \textcolor{red}{- 9 x} + 81$

$- 3 y = - \textcolor{red}{- 9 x} + 81$

$\frac{- 3 y}{\textcolor{g r e e n}{- 3}} = \frac{\textcolor{red}{- 9 x} + 81}{\textcolor{g r e e n}{- 3}}$

$\frac{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{g r e e n}{- 3}}} = \frac{\textcolor{red}{- 9 x} + 81}{\textcolor{g r e e n}{- 3}}$

$y = \frac{\textcolor{red}{- 9 x} + 81}{\textcolor{g r e e n}{- 3}}$

$y = \frac{\textcolor{red}{- 9 x}}{\textcolor{g r e e n}{- 3}} + \frac{81}{\textcolor{g r e e n}{- 3}}$

$y = 3 x - 27$

Therefore the slope is $\textcolor{red}{3}$ and the y-intercept is $\textcolor{b l u e}{- 27}$ or ($\textcolor{b l u e}{0 , - 27}$)