# What is the slope and y-intercept of the line 2x - 3y = -18?

Jul 29, 2015

slope $= \frac{2}{3}$
and\y-intercept $= 6$

#### Explanation:

Slope
For an equation in the form:
$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$
the slope is
$\textcolor{w h i t e}{\text{XXXX}}$$m = - \frac{A}{B}$
for the given equation $2 x - 3 x = - 12$ this becomes
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{2}{3}$

Alternatively we could rewrite the given equation $2 x - 3 y = - 18$
into "slope intercept" form:
$\textcolor{w h i t e}{\text{XXXX}}$$y = m x + b$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$where $m$ is the slope and $b$ is the y-intercept
$\textcolor{w h i t e}{\text{XXXX}}$2x-3y = -18#

$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$- 3 y = - 2 x - 18$

$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$y = \frac{2}{3} x + 6$

y-intercept
If you rewrote the equation in "slope intercept form" (see above)
the slope can be read directly from the equation as
$\textcolor{w h i t e}{\text{XXXX}}$$m = 6$

Otherwise
note that the y-intercept is the value of $y$ when $x = 0$ in the equation:
$\textcolor{w h i t e}{\text{XXXX}}$$2 \left(0\right) - 3 y = - 18$
$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$y = 6$