How to Graph Linear Equations Using Three Points
Linear equations are among the most important concepts in precalculus coursework. Graphs of linear equations provide a connection between algebra and geometry by using equations to create a straight line. Graphing a linear equation can be done a number of ways, one of which is plotting three separate points on a Cartesian coordinate system, and using these points to create a line described by the linear equation. This can be done in a few short steps.
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Instructions
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Find three points, or ordered pairs, described by the linear equation. This is done by choosing three x values and plugging them into the linear equation to find the corresponding y values. For example, if the linear equation is
y = 4x - 3,
and the three x values you chose are 0, 2 and 5, plugging these numbers into the equation yields
y = 4(0) - 3 = -3
y = 4(2) - 3 = 5
y = 4(5) - 3 = 17.
Therefore, the ordered pairs are (0, -3), (2, 5) and (5, 17).
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2
Plot the three ordered pairs that you calculated on a Cartesian coordinate system on the graph paper. For example, to plot the point (0, -3), you find the single point where x = 0 and y = -3. Draw a dot where this point occurs.
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3
Use the ruler to draw a straight line that goes through all three points. In the example, this is the line that is described by the linear equation y = 4x - 3.
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References
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