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How to Graph Inequalities in Two Variables Using Decimals

Linear equations graph as a straight line that is based on the equation's slope intercept form. Slope intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept, or point where the slope intersects the y-axis. Linear inequalities work similarly to linear equations, except that the "equals" sign of the equation is replaced by an inequality symbol. The inequality symbols are > ("greater than"), < ("less than"), ≥ ("greater than or equal to") and ≤ ("less than or equal to").

Instructions

- 1
  Graph the linear inequality 2y > 6x + 3. Divide both sides by 2 to convert to slope intercept form: y > 3x + 1.5 . Note that the slope is 3 and the y-intercept is 1.5, or point (0, 1.5).
- 2
  Draw a dot on the graph at the point of the y-intercept. Find four additional points for the line using the slope of 3 to move the y-intercept point up three spots on the y-axis and over one spot on the x-axis: i.e., (0, 1.5) becomes (1, 4.5). Apply the slope again for three more points: (1 + 1, 4.5 + 3) = (2, 7.5); (2 + 1, 7.5 + 3) = (3, 10.5) and (3 + 1, 10.5 + 3) = (4, 13.5).
- 3
  Plot the new points on the graph. Draw a dotted line to connect all of the points, drawing arrows on each end of the line to indicate continuation. Note that the line is dotted because there was no "equals to" in the inequality symbol, so the points on the line are not included in the solution set. Shade the area of the graph above the line since the inequality symbol was "greater than."

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