Graphing Inequalities

Definition:  The process to graph linear inequalities is very similar to graphing linear equations. First, we will graph the line considering it as an “equals” line. Then we will shade in the appropriate area.

Example: Graph: -4x + 2y ≤ -2

Solution: 

Step 1: Rearrange the equation so “y” is on the left and everything else is on the right. Here we will add “4x” to both sides and then divide by “2”. This gives us: y ≤ 2x – 1.

Step 2: Plot the “y=” line (making the line solid for “y≤” or “y≥”, and a dotted line for “y<” or “y>”).

Step 3: Shade above the line for a “greater than” or below the line for a “less than”.

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