# How do you write 2x-3y= 15 in slope-intercept form and graph it?

Mar 24, 2017

$y = \frac{2}{3} x - 5$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$\text{Rearrange " 2x-3y=15" into this form}$

subtract 2x from both sides.

$\cancel{2 x} \cancel{- 2 x} - 3 y = - 2 x + 15$

$\Rightarrow - 3 y = - 2 x + 15$

divide ALL terms on both sides by - 3

$\frac{\cancel{- 3} y}{\cancel{- 3}} = \frac{- 2}{- 3} x + \frac{15}{- 3}$

$\Rightarrow y = \frac{2}{3} x - 5 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

The y-intercept is - 5$\leftarrow \textcolor{red}{\text{ 1 point on the graph}}$

$\text{choose " x=3" and find y}$

$x = 3 \to y = \left(\frac{2}{3} \times 3\right) - 5 = 2 - 5 = - 3$

$\Rightarrow \left(3 , - 3\right) \leftarrow \textcolor{red}{\text{ is a point on the graph}}$

Plot the 2 points and draw a straight line through them and you have the graph.
graph{2/3x-5 [-10, 10, -5, 5]}