# How do you graph  -3x-2y=-2?

Jun 21, 2017

Convert the given equation to slope intercept form, $y = m x + b .$ Determine points on the line. Plot the points and draw a straight line through them.

#### Explanation:

Graph:

$- 3 x - 2 y = - 2$

Solve for $y$ to get the equation into slope intercept form: $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept (the value of $y$ when $x = 0$).

Add $3 x$ to both sides of the equation.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - 2 y = 3 x - 2$

Simplify.

$- 2 y = 3 x - 2$

Divide both sides by $- 2$.

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

A negative number divided by another negative number gives a positive result.

$y = - \frac{3}{2} x + 1$

Now you can determine several points on the line by choosing values for $x$ and solving for $y$.

Points

$x = - 2 ,$$y = 4$

$x = 0 ,$$y = 1$

$x = 2 ,$$y = 2$

Plot the points and draw a straight line through them.

graph{-3x-2y=-2 [-10, 10, -5, 5]}