How to Graph Linear Equations With Two Variables

by UrielA, Demand Media

A linear equation can be written in the form ax + by = c, where x and y are variables and a, b, and c are real numbers. Although many modern graphing calculators can graph linear equations (in any form) with minimal work on your part, graphing linear equations is a basic math skill that you should learn.

Use the Solutions to Graph the Equation

Step 1

Substitute x=0 in the equation and find a value for y that makes the resulting equation true. For example, in the equation x-2y=2, when x=0, the equation becomes -2y=2. Since y=-1 makes this equation true, one point on the line is (0,-1). The x-value is the first coordinate. The y-value is the second coordinate.

Step 2

Substitute y=0 in the equation and find a value for x that makes the resulting equation true. Following the example in Step 1, when y=0, the equation x-2y=2 becomes x=2. Thus, another point on the line is (2,0).

Step 3

Find a third point on the line. Substitute any value for x or y that is not already listed and solve for the other variable. For instance, when y=1, the equation x-2y=2 reduces to x-2=2 or x=4. A third point on the line is (4,1).

Step 4

Plot the three points on a coordinate plane. Draw a line through the three points.

Tips

  • You only need two points to draw a line. However, the third point serves as a check—-if you found the points correctly, the three points form a line.
  • If Step 2 gives you the same point as Step 1, try another value for y.

References

  • "Integrated Algebra 1"; Ann Xavier Gantert; 2007

About the Author

Uriel Avalos is an editor based in NY. He works for a textbook publishing company that makes high school textbooks. Uriel has an MA in Mathematics and a BA in Computer Science and Mathematics. He is passionate about math and technology.

Photo Credits

  • Jupiterimages, Brand X Pictures/Brand X Pictures/Getty Images