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How to Write an Inequality for a Graph

Graphing equations is one of the fundamental skills associated with algebra. When you're graphing a linear equation, you end up with a solid line going through at least two plotted points. Inequalities are somewhat different. Instead of telling you what y is, an inequality tells you what y is not, and then gives you the parameters for all of the solutions that y can include. The process for graphing an inequality is virtually identical to graphing an equation, though. Using a T chart, you can plot points and draw the parameter that will show your solutions.

Instructions

    • 1

      Write an equation with an exponential degree of 1. An example of this is: y = 2x + 6.

    • 2

      Erase the equals sign and replace it with a less-than (<) sign. Now the example reads: y < 2x + 6. This means that for every x, y is everything less than the sum of 2x + 6. If x = 0, y is everything less than 2(0) + 6, or y < 6 at x = 0.

    • 3

      Draw x and y axes on a piece of graph paper and mark a circle at the ordered pair (0,6). Don't draw a solid circle --- 6 is actually not part of the solution. Everything less is, including 5.999, but not 6; so leave the circle open.

    • 4

      Make a T chart and label the left side "x" and the right side "y." Put "0" and "6" in the first row. Then, write the numbers 1 through 4 down the x column. Solve each for y. In the example, you'll have 8, 10, 12 and 14 across from 1, 2, 3 and 4. Mark circles at each of those ordered pairs.

    • 5

      Draw a dotted line through the four points and extending straight outward in both directions. Put arrow ends on both ends to show that the line goes on infinitely. Then, shade in the part of the graph below the dotted line. You're indicating that the area of solution for y is the entire area beneath, but not including, the dotted line. If there had been a line under the < sign in your inequality, that would indicate that y is less than or equal to 2x + 6. In that case, you would use solid points and a solid line, in addition to shading.

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