Summarizing Graphs of Linear Inequalities

Summarizing Graphs of Linear Inequalities

Key Concepts

• To Graph a Linear Inequality
  1. Identify and graph the boundary line.
     If the inequality is \(\le \text{or}\ge \), the boundary line is solid.
     If the inequality is < or >, the boundary line is dashed.
  2. Test a point that is not on the boundary line. Is it a solution of the inequality?
  3. Shade in one side of the boundary line.
     If the test point is a solution, shade in the side that includes the point.
     If the test point is not a solution, shade in the opposite side.

Glossary

boundary line

The line with equation \(Ax+By=C\) that separates the region where \(Ax+By>C\) from the region where \(Ax+By

linear inequality

An inequality that can be written in one of the following forms:

\(\begin{array}{cccccccccc}\hfill Ax+By>C\hfill & & & \hfill Ax+By\ge C\hfill & & & \hfill Ax+By

where \(A\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}B\) are not both zero.

solution of a linear inequality

An ordered pair \(\left(x,y\right)\) is a solution to a linear inequality the inequality is true when we substitute the values of x and y.