Graphing Linear Inequalities

To graph a linear inequalities rewrite the inequality in the y = mx + b form and graph 3 points using the slope (m) and the y-intercept (b.)  Before you draw the line connecting the points observe the inequality.  If the inequality is £ or ³, use a solid line to connect the points on the line.  If the inequality is > or <, use a slashed or dotted line to connect the points on the line.  Next, you will have to choose whether the solution lies “above” the line or to the right (if the inequality is > or ³) or whether the solution lies “below” the line or to the left (if the inequality is < or £).  You may also decide to test a point.  Pick a point that is not on the line and substitute the test point into the inequality (it is best if you substitute the point into the original, unchanged inequality.)  If the inequality is true using the test point, then shade the region where the test point lies.  If the inequality is false using the test point, then shade the region on the opposite side of where the test point lies.

When solving a system of linear inequalities, graph both inequalities onto one coordinate axis and shade each inequality appropriately.  Once you have graphed both inequalities, note the intersection (overlapping) of the two graphs.  The intersection will be the solution.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 19-Sep-2007