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Graphing a Linear Equation by Plotting Points
The Point-Plotting Method is a systematic three-step procedure for graphing any linear equation in two variables:
- Find three solution points. Choose three values for one of the variables (typically , especially when is already isolated on one side of the equation), substitute each value into the equation, and solve for the other variable. Organize the resulting ordered pairs in a table.
- Plot the points on a rectangular coordinate system. Mark each ordered pair on the grid and verify that all three points fall on the same straight line. If they do not line up, one or more calculations contain an error that must be corrected.
- Draw the line. Connect the points with a straight line, extend it to fill the grid, and place arrows on both ends to indicate the line continues infinitely in each direction.
Although only two points are mathematically required to determine a line, plotting a third point serves as a built-in check: if any one of the three points is incorrect, the points will not be collinear, signaling a mistake. With only two points, an error in one of them would still produce a line — but it would be the wrong line, with no visual warning that something went wrong.
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