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How to Graph Inequalities in Two Variables With Fractions

Linear equations graph as a straight line based off the slope intercept form of y = mx + b, where "m" is the slope of the line and "b" is the y-intercept where the line crosses the y-axis of the graph. Linear inequalities work similarly to the equations, except the equal sign is replaced by an inequality symbol. The inequalities result in a straight line, but it can be dotted or solid based on the inequality symbol. The solution set is then shaded based on the symbol.

Instructions

- 1
  Convert a linear inequality to slope intercept form to begin the graphing process. Convert (1/2)y ≤ (1/4)x + 2, for example, by multiplying 2 to both sides: y ≤ (2/4)x + 4. Simplify the fraction: y ≤ (1/2)x + 4 where the slope is (1/2) and the y-intercept is 4 or point (0, 4).
- 2
  Solve the right side of the inequality for four different values of "x", two negative and two positive, to get an accurate view of how the line is shaped. Use -2, -1, 1 and 2 for the example inequality. Solve for -2: (1/2)(-2) + 4 = -1 + 4 = 3 or point (-2, 3). Solve for -1: (1/2)(-1) + 4 = -(1/2) + 4 = -(1/2) + (8/2) = -7/2 = -3.5 or point (-1, -3.5). Solve for 1: (1/2)(1) + 4 = (1/2) + 4 = (1/2) + (8/2) = (9/2) = 4.5 or point (1, 4.5). Solve for 2: (1/2)(2) + 4 = 1 + 4 = 5 or point (2, 5).
- 3
  Graph the found points, including the y-intercept. Draw a solid line if the inequality includes an "equals to" or, if it doesn't, a dotted line. Shade the area above the line if the inequality symbol is "greater than" or below the line for "less than". Note that since the inequality symbol in the example was ≤, the graph will have a solid line with a shaded solution set below the line.

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