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How to Graph Inequalities in Algebra 2

Unlike an equation, an inequality refers to a problem in which the solution is a group of real numbers, rather than just one real number. The basic forms of inequalities are mathematical statements such as "2 < 3" and "3.467 > 3.466." More complex versions of inequalities involve variables; by graphing these inequalities, you can visualize their solutions.

Instructions

- 1
  Replace the inequality with an equal sign to make the inequality an equation. For example, with the inequality "2x + y > 4," make it "2x + y = 4."
- 2
  Convert the equation to slope-intercept form by isolating the "y" in the equation. Using the associative property for regrouping, the equation "2x + y = 4" becomes "y = -2x + 4," which you obtain by subtracting "2x" from both sides of the equation.
- 3
  Substitute "x" for a random number, solve for "y" and record the answer. Use the "y" answer you found with the "x" number you plugged in to form coordinates. Repeat this step at least two more times. For the example problem, let x = 2 and 3. For X = 2, y = -2(2) + 4; thus, y = 0. For x = 3, y = -2(3) + 4; thus, y = -2.
- 4
  Plot the x,y coordinates you found on graphing paper and then draw a line connecting all the points to graph the equation. You can use the points (2, 0) and (3, -2) for "2x + y > 4"
- 5
  Shade the area below the line if the inequality is "<" (less than) or above the line if it is ">" (greater than). Follow this rule for shading even if the inequality involves a "≤" (less than or equal to) or "≥" (greater than or equal to) sign. In the inequality "2x + y > 4," you would shade the area above the line.

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