Graphing Linear Inequalities – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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After you have mastered writing and graphing linear equations, it’s time to move on to writing and graphing linear inequalities. This starts out the same as graphing linear equations but quickly veers into new territory.

Just like graphing an equation, to graph a linear inequality, first manipulate the inequality so it’s in slope-intercept form, y = mx + b, by using opposite operations and isolating the y-value. But, different from equations, don’t forget to pay attention to any needed sign changes. If you multiply or divide by a negative number, remember to flip the sign. Once you have done that, using the y-intercept as your first point, use the slope to draw in additional points.

Before you draw a line to connect the dots, take a look at the inequality symbol, for less than or greater than – use a dotted line. For less than and equal to and greater than and equal to – use a solid line. Now shade in the solution set. As a rule, greater than is above the line, and less than is below the line but depending on the slope of the line, this may not be so obvious, so pick a test point and verify that the solution set works before you highlight the area in permanent ink. To see some real world uses of linear inequalities and learn some tips to make graphing easier, take a look at this fun video.

Write equations of the line.


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Exercises in this Practice Problem
Decide which graph describes the given situation.
Determine which graph corresponds to which inequality.
Decide which values would earn aunt Sally enough money.
Decide which graph corresponds to the given inequality.
Summarize how you can recognize the solution depending on the inequality sign.
Decide if the given points lie within the area described by the inequalities.