# How do you graph 3x+y<5?

Jun 22, 2015
1. The first step is to treat the inequality as an equality.
$3 x + y = 5$

2. Then find coordinates that will create the border of the area that is represented by the inequality.
(I usually rewrite the equation into slope-intercept form
$y = - 3 x + 5$ and graph that.)

3. Instead of graphing a straight line use a dotted line, since the original inequality $3 x + y < 5$ is less than rather then less than or equal.
graph{3x + y < 5 [-10, 10, -5, 5]}

4. To decide which side of the line to graph, pick a coordinate pair on either side of dotted line. (I usually use $\left(0 , 0\right)$ ) and see if it makes the inequality true.
ex. Is $\left(0 , 0\right)$ part of the solution set ?
$3 x + y < 5$
$3 \left(0\right) + 0 < 5$
$0 < 5$ is a true statement so the left side of the dotted line should be shaded