What is the slope and y intercept of 6x - 3y = 12?

Aug 22, 2015

Answer:

$y = 2 x - 4$

Explanation:

The slope-intercept form for a general line $y$ looks like this

$\textcolor{b l u e}{y = m x + b} \text{ }$, where

$b$ - the $y$-intercept;
$m$ - the slope of the line.

Your starting equation is

$6 x - 3 y = 12$

To get it to slope-intercept form, isolate $y$ on one side of the equation.

You can do that by adding $- 6 x$ to both sides of the equation

$\textcolor{red}{\cancel{\textcolor{b l a c k}{6 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{6 x}}} - 3 y = 12 - 6 x$

$- 3 y = - 6 x + 12$

Now divide all the terms by $- 3$ to get

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} \cdot y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}}} = \frac{\left(- 6\right)}{\left(- 3\right)} x + \frac{12}{\left(- 3\right)}$

$\textcolor{g r e e n}{y = 2 x - 4}$