EDGE Math 8

Graphs of Linear Inequalities in Two Variables

Example 1

Graph the inequality $2 x + y < 6.$

Solution

First, graph the boundary line whose equation is $2 x + y = 6.$ Since the inequality symbol is <, the boundary line is a dashed line.

Then, to make the computation easier, choose $(0, 0)$ as the test point; that is, substitute 0 for x and 0 for y in the inequality $2 x + y < 6.$

$2 (0) + 0$	$< 6$
$0$	$< 6$		True

Since $(0, 0)$ satisfies the given inequality, shade the region on the side of the boundary line that includes the point $(0, 0).$ Refer to the shaded region in the figure below for the graph of $2 x + y < 6.$