Math Playground
Algebra

Graphing inequalities

Shade the half-plane below or above — and the boundary line tells you which.

On a number line: open circle for strict (<, >), filled circle for inclusive (≤, ≥). On a plane: shade the half above or below the boundary line.

Drag the sliders
-8-426
y = m·x + b

Turning a line into a region

  • Graph the boundary line y = mx + b (this widget shows it).
  • Dashed line for strict < or > (boundary not included); solid for ≤ or ≥.
  • Shade above the line for y > / y ≥; below for y < / y ≤.
  • Unsure which side? Test (0, 0): if it satisfies the inequality, shade that side.
Your turn

Describe the graph of y ≤ −x + 3.

On a one-variable number line instead: open circle for < or >, filled circle for ≤ or ≥, arrow pointing toward the solutions.

Try it

Graph y > 2x + 1

Dashed line y = 2x + 1, shade above.