# How do you graph 2x-3y<=6?

Apr 22, 2015

Solve $2 x - 3 y \le 6$ for y.

Subtract 2x from both sides.

$- 3 y \le - 2 x + 6$

Divide both sides by -3. This will reverse the $\le$ symbol to $\ge$.

$y \ge - \frac{2}{-} 3 x - \frac{6}{3}$=

$y \ge \frac{2}{3} x - 2$

Determine two points on the line by using the equation making $y = \frac{2}{3} - 2$.

If $x = 0 , y = \frac{2}{3} \cdot 0 - 2 = 0 - 2 = - 2$ Point = $\left(0 , - 2\right)$
If $x = 3 , y = \frac{2}{\cancel{3}} \cdot \cancel{3} - 2 = 2 - 2 = 0$ Point = $\left(3 , 0\right)$

Plot the two points and draw a straight line through them. Then shade in the area above the line.
graph{y>=2/3x-2 [-10, 10, -5, 5]}