How to Graph Linear Inequalities in Two Variables for 8th Grade Math
A linear inequality incorporates the properties of a line and an area related to that line. The two forms of linear equations are "y<mx+b" or "y>mx+b." The first equation means that the value of "y" is less than the amount calculated on the right side of the inequality, and the second one means reads that "y" is greater than that amount. Learning to graph linear inequalities correctly can set the stage for increased understanding of other eighth grade math concepts.
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Instructions
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1
Substitute a value for the "X" variable of the equation to calculate the inequality's "Y" variable value. For example, for the equation "y<3x-2," substituting the value of "2" for the "X" results in the inequality's "Y" variable equaling "y<4," which is "y" is less than four.
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2
Substitute a second value into the "X" variable to calculate another of the inequality's "Y" variable value. For this example, substituting the value of "-6" for the "X" variable results in the inequality's "Y" variable equaling "y<-20."
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3
Select two perpendicular lines that cross in the middle of the graph paper. These two lines are the graph's axes. The vertical one is the "Y" axis and the horizontal one is the "X" axis.
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4
Plot a point using the "X" and "Y" values in step 1 on the graph. For "X" values, if the value is positive, move that many lines to the right of the "Y" axis, and for negative values, move that many lines to the left of the "Y" axis. For this example, the "X" value is "2" and is positive, so it will be located two lines left of the "Y" axis. For "Y" values, positive values are that many lines above the "X" axis, and negative values are that many below. For this example, the "Y" value is 4, so it will be located four lines above the "X" axis. Find the point where these two lines cross, and place a point on that intersection to represent the two values.
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5
Plot a second point using the method described in step 4 with the "X" and "Y" values calculated in step 2. For this example, the "X" value is "-6" and the "Y" value is "-20." The point is located where the sixth line to the left of the "Y" axis intersects the twentieth line below the "X" axis. Draw arrows on the ends of the line to signify that the line continues in each direction.
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6
Draw a straight line comprised of dashes, like "- - - - -," through the two points using the straight edge of the ruler. If the inequality has the "<" symbol, which means less than, then shade the area underneath the line. If the inequality has the ">" symbol, which means greater than, then shade the area above the line. For this example, the area below the line would be shaded. Shading the area means that the inequality includes that entire area.
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Tips & Warnings
If the inequality has the "<=" symbol, which means less than or equal, or ">=", which means greater than or equal, then draw a solid line through the points instead of a line of dashes.
