# How do you graph the inequality 2x-3y<=1 on the coordinate plane?

Apr 26, 2017

Draw the line and decide which side to shade for the required region.

#### Explanation:

Treat the inequality as a straight line graph first .
Then shade the correct side of the line to indicate the solutions which are less than $1$

You can use any method to draw the straight line - plot points or use the intercept/gradient method.

I will use the method of the $x \mathmr{and} y$ intercepts.

To find the $x$-intercept, make $y = 0$

$2 x - 3 y = 1 \text{ } \rightarrow 0 - 3 y = 1$

$\textcolor{b l u e}{y = - \frac{1}{3}}$

To find the $y$-intercept, make $x = 0$

$2 x - 3 y = 1 \text{ } \rightarrow 2 x - 0 = 1$

$\textcolor{b l u e}{x = \frac{1}{2}}$

Now that you have both intercepts you can plot them and draw a solid line through them. This is the line $2 x - 3 y = 1$

You could also write the equation as : $y = \frac{2}{3} x - \frac{1}{3}$

To decide which side of the line to shade, choose a test point.

$\left(0 , 0\right)$ is a good one.

$2 x - 3 y \le 1 \text{ "rarr" " 0-0 <=1" "rarr" } 0 \le 1$ is true.

$\therefore \left(0 , 0\right)$ is in the required region and the area ABOVE the line must be shaded. graph{2x-3y<=1 [-10, 10, -5, 5]}