Graphing Linear Inequalities

Property To graph an inequality, graph the boundary line (solid or dashed). Then, use a test point, often $(0, 0)$, to decide which half plane to shade. If the test point makes the inequality true, shade its entire region. Explanation First, draw your line—solid for 'or equal to,' dashed for not. Then, pick a test point not on the line, like $(0,0)$. If it makes the inequality true, shade its whole side! If it's false, you shade the other side. It’s all about finding the 'true' zone! Examples Graph $y < x + 2$. Draw a dashed line for $y = x + 2$. Test $(0, 0)$: $0 < 0 + 2$ is true. Shade the half plane containing $(0, 0)$. Graph $y \ge 2x + 1$. Draw a solid line for $y = 2x + 1$. Test $(0, 0)$: $0 \ge 2(0) + 1$ is false. Shade the half plane that does not contain $(0, 0)$.