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Graphing Linear Inequalities in Two Variables

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( and ), graph a solid line.

Finally, pick one point not on the line ( ( 0 , 0 ) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.


Graph the inequality y 4 x 2 .

This line is already in slope-intercept form , with y alone on the left side. Its slope is 4 and its y -intercept is 2 . So it's straightforward to graph it. In this case, we make a solid line since we have a "less than or equal to" inequality.

Now, substitute x = 0 , y = 0 to decide whether ( 0 , 0 ) satisfies the inequality.

0 ? 4 ( 0 ) 2 0 ? 2

This is false. So, shade the half-plane which does not include the point ( 0 , 0 ) .