How to Find Linear Equations From Graphs
A linear equation, when graphed, produces a straight line. These graphs can be useful for visually presenting sales predictions. If you only have the graph, however, you can also work backward to find the linear equation that created the graph. Each linear equation has two distinguishing characteristics: the slope and the y-intercept. Once you have found both of these features for a graph, you can find the linear equation that the graph represents.
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Instructions
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Find the x- and y-coordinates of two points on the line on the graph. For example, you might notice the line goes through (5, 3) and (7, 7).
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Subtract the second y-coordinate from the first y-coordinate. In this example, you would subtract 7 from 3 to get negative 4.
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Subtract the second x-coordinate from the first x-coordinate. In this example, you would subtract 7 from 5 to get negative 2.
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Divide the difference in the y-coordinates by the difference in the x-coordinates to find the slope and call this m. In this example, you would divide negative 4 by negative 2 to get 2 as the slope, or m.
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Find the y-coordinate where the line crosses the y-axis and call this "b." In this example, the line would cross the y-axis when the y-coordinate equals -7, so -7 would be your y-intercept, or b.
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Plug m and b into the formula y = mx + b to find the linear equation from a graph. In this example, since "m" equals 2 and "b" equals negative 7, you would get y = 2x - 7.
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References
- Photo Credit graph from money image by Anatoly Tiplyashin from Fotolia.com
