Graphing Linear Inequalities

Graphing a linear inequality in two variables

Step 1 — Graph the boundary line $y = mx + b$. Use a dashed line for strict ($>$ or $<$) and a solid line for non-strict ($\geq$ or $\leq$).

Step 2 — Choose a test point (usually $(0, 0)$) and plug it into the inequality. If it satisfies the inequality, shade the side containing the test point. If not, shade the other side.

Step 3 — Shade the solution region. For $y > mx + b$: shade above the line. For $y < mx + b$: shade below.

Example: $y > 2x - 3$

Draw $y = 2x - 3$ as a dashed line. Test $(0, 0)$: $0 > 2(0) - 3 = -3$? Yes → shade the side containing $(0, 0)$ (above the line).

Try it in the visualization

Adjust slope, intercept, and inequality type. The boundary line switches between dashed/solid. The shaded region shows all solutions. Test points verify which side satisfies the inequality. Solid for $\geq$), then shade the region above the line. Every point in the shaded region satisfies the inequality.