Constant Rate of Change and Slope

Rule

Slope Formula

The slope of a line can be found algebraically using the following rule.

m=y_2-y_1/x_2-x_1

Here, (x_1,y_1) and (x_2,y_2) are two points on the line.

Proof

To prove the slope formula, use the following definition of slope. m=change in y -value/change in x -value Consider a line passing through the points (x_1,y_1) and (x_2,y_2).

Notice that the change in y-value is the difference between the y-coordinates of the points as well as the change in x-value is the difference between the x-coordinates.

From here, the slope formula can be found by substituting y_2-y_1 and x_2-x_1 for the change in y-value and the change in x-value, respectively. m=change in y -value/change in x -value ⇓ m=y_2-y_1/x_2-x_1

Exercises
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