Linear inequalities can be solved graphically. By using a table of values, you can graph a line to represent your inequality. Graphs help to show the set of solutions possible for an inequality. Instead of just seeing an answer, you can see a picture of the solution, making it easier to understand.
Instructions
1. Write down your inequality.
2. Solve your inequality for x or y. You can solve for either as long as you are consistent. Normally, you solve for x.
3. Create a table of values for y. Normally, you will choose three values. Three points are all that is needed for straight lines. You can choose any three values you wish. If your inequality solved with fractions, you may want to choose values divisible by the denominator or anything to turn the fraction into a whole number. Zero is also a good choice for a value.
4. Solve your inequality for each value of y you chose. When solving, you can replace the inequality symbol with an =.
5. Graph the points on your graph paper and connect the dots using a ruler.
6. Determine where to shade the graph. Choose a point above or below your line. Substitute your point in place of the x and y in your original inequality. If the point makes your inequality true, then shade that side of the line. If the point makes your inequality false, then shade the opposite side of the line.
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