Question

How do I graph a linear inequality in two variables?

Answer 1

A linear inequality is in the form:

`ax + by > c` or ax + by < c.

First, graph the line ax + by - c = 0 by the 2 y-intercepts and x-intercepts.

Then find the area (above or below the line) that make the inequality true. You may use the origin O (0, 0) as test point

Example. Solve: 2x + 3y > -4

First, graph the line 2x + 3y + 4 = 0 by the 2 x and y intercepts.
Make x = 0 -> 3y = -4 -> y = -4/3
Make y = 0 -> 2x = -4 -> x = -2
Solve the inequality: f(x) = 2x + 3y + 4 > 0 by using origin O (0, 0) as test point. We get 4 > 0, It is true, then the area above the line is the solution set.
graph{2x + 3y + 4 = 0 [-10, 10, -5, 5]}