# How do you graph 2y-6x=10?

Apr 22, 2017

See the explanation.

#### Explanation:

Graph:

$2 y - 6 x = 10$

You can convert this equation into slope-intercept form by solving for $y$. Slope-intercept form is: $y = m x + b$, where $m$ is the slope of the line, and $b$ is the y-intercept when $x = 0$.

Factor out the common term $2$.

$2 \left(y - 3 x\right) = 10$

Divide both sides by $2$.

$\frac{2 \left(y - 3 x\right)}{2} = \frac{10}{2}$

Simplify.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(y - 3 x\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{10}^{\textcolor{b l u e}{5}}}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{2}^{\textcolor{b l u e}{1}}}}}}$

$y - 3 x = 5$

Add $3 x$ to both sides.

$y - 3 x + 3 x = 5 + 3 x$

Simplify.

$y - \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} = 5 + 3 x$

$y = 3 x + 5$

The slope is $3$ and the y-intercept is $5$. The y-intercept is the point $\left(0 , 5\right)$. The slope is $\frac{3}{1}$. So you can place a point at the y-intercept and move up $3$ places and over to the right $1$ to get another point. You can also go down $3$ places and over to the left $1$ place to get another point.

You can also determine ordered pairs using the equation.

$x$$\textcolor{w h i t e}{\ldots \ldots . .}$$y$
$0 , \textcolor{w h i t e}{\ldots \ldots .} 5$
$2 , \textcolor{w h i t e}{\ldots \ldots .} 11$
$4 , \textcolor{w h i t e}{\ldots \ldots .} 17$

graph{y=3x+5 [-18.95, 13.1, 1.03, 17.04]}