Key Concepts

Verifying a solution of a Linear Inequality The ordered pair [latex](x,y)[/latex] is a solution of a linear inequality if, when the values are plugged into the linear inequality, the statement remains true.

Graphing Linear Inequalities  To graph an inequality,

• Graph the related boundary line. Replace the <, >, ≤ or ≥ sign in the inequality with = to find the equation of the boundary line.
• Identify at least one ordered pair on either side of the boundary line and substitute those [latex](x,y)[/latex] values into the inequality. Shade the region that contains the ordered pairs that make the inequality a true statement. 
• If points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for ≤ or ≥ inequalities.
• If points on the boundary line aren’t solutions, then use a dotted line for the boundary line. This will happen for < or > inequalities.