Graphing Linear Inequalities

Linear inequalities in two variables are of the form :

ax+ by ≤ c,

where ≤ can be replace with ≥, < or >.

To graph a linear inequality :

1. Write the inequality as an equation .
2. Find at least two points on the line, plot the points and sketch the line. The line will be solid if the inequality is ≤ or ≥ and dashed if the inequality is < or >.
3. Test a point not on the line to determine which half plane will be shaded.

Example: Determine the solution set for the following inequality.
y< x–3

Example: Determine the solution set for the following inequality .
2x–5y ≥10

Example: Determine the solution set for the following inequality .
y ≤ 4

Example: Determine the solution set for the following inequality .
x> -1

Example: Determine the solution set for the following inequality .
8x + 4y > 0