# How do you write 2x - 3y > 7 in slope intercept form?

Aug 7, 2015

The boundary can be written in slope-intercept form giving
$\textcolor{w h i t e}{\text{XXXX}}$$y < \frac{2}{3} x + \left(- \frac{7}{3}\right)$

#### Explanation:

given $2 x - 3 y > 7$

adding $3 y$ to both sides
$\textcolor{w h i t e}{\text{XXXX}}$$2 x > 3 y + 7$

subtracting 7 from both sides
$\textcolor{w h i t e}{\text{XXXX}}$$2 x - 7 > 3 y$

dividing both sides by $3$
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{2}{3} x - \frac{7}{3} > y$

Reversing the sides
$\textcolor{w h i t e}{\text{XXXX}}$$y < \frac{2}{3} - \frac{7}{3}$

or (in explicit slope-intercept form
$\textcolor{w h i t e}{\text{XXXX}}$$y < \left(\frac{2}{3}\right) x + \left(- \frac{7}{3}\right)$
where the boundary line has a slope of $\frac{2}{3}$ and a y-intercept of $\left(- \frac{7}{3}\right)$