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Graphs of Linear Equations in Two Variables
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Slope of a Line

Example

Find the slope of the line passing through the points (−2,  7) and (3,  −3).



Solution

Let ( x 1 ,   y 1 )=(−2,  7) and ( x 2 ,   y 2 )=(3,  −3). The slope of the line that passes through these points is

m= y 2 − y 1 x 2 − x 1 = −3−7 3−(−2) = −10 5 =−2.

The figure below shows the given line

Notice that in this line, every vertical change of –2 units (which is the rise) corresponds to a horizontal change of 1 unit (which is the run). In general, when a line falls from left to right, it has a negative slope.