Graphing Linear Inequalities on a Coordinate Plan
Graphing inequalities is typically the same as graphing an equation in slope-intercept form, except instead of an equal sign, there is a greater than >, less than <, or equal to < / > sign. So, lets solve the example equation to the left. First, you must find the X and Y-intercepts. As explained on the previous page, set Y equal to 0 to find X and vice versa to find Y. After doing so, you'd find that the X-int = 2 and the Y-int = -1. Once you mark both of the points you connect them with a dotted line, because there is not an 'equal to' in the inequality. The line is now drawn, and because it's an inequality, you must shade a side of the line. To find which area to shade you plug in a point to test if it works, I will try (0,0). The tested inequality would be 0-2(0) > 2 or 0>2. Obviously, 0 is not greater than 2, so the coordinate (0,0) does not work. Therefore, you would shade away from that point, which would be to the bottom of the line.
This example is more complicated because there are three lines. The three inequalities are: Y < 3, X < 2 and Y > -1/3 X. The first line is solid, its a horizontal line at 3 on the Y-intercept, and the shading is below the boundary. The second line is dashed, its a vertical line at 2 on the X-intercept, and shading is to the left side of the boundary line. Finally, the third line is solid, it descends 1 over 3, and the shading is above. The system of the inequalities is highlighted in pink, where it shows the region of the coordinate plan where the three lines shadings overlap.