3.2.1 Finding the Slope Given Two Points Key Objectives • Learn to find slope by using the slope formula. Key Terms

• The rise is the difference in the y -values of two points on a line. • The run is the difference in the x -values of two points on a line. • The slope of a line is a measure of its steepness and is the ratio of rise to run.

The formula given above can be used to calculate the slope of a line when the coordinates of two points on the line are known. The letter m is used to represent slope. The coordinates of two points on the line are represented by y 2 , y 1 , x 2 , and x 1 , where y 2 is the y -coordinate of the second point, x 2 is the x -coordinate of the second point, and so on. Example 1 To find the slope of a line, substitute the coordinate values from two points on that line into the slope formula and simplify. It does not matter which point is designated as ( x 1 , y 1 ) and which point is designated as ( x 2 , y 2 ).

In this example, (5, − 3) is designated as ( x 1 , y 1 ) and ( − 1, 2) is designated as ( x 2 , y 2 ). However, the slope may also be found by designating ( − 1, 2) as ( x 1 , y 1 ) and (5, − 3) as ( x 2 , y 2 ). To demonstrate this, find the slope again, using this point designation. 5 6 The slope is again − 5/6. The order in which the points are chosen is irrelevant because the line is the same no matter which point is chosen as ( x 1 , y 1 ). = − − 3 2 5 ( 1) − − = − =− m 5 6 NOTE: Do not designate the x -coordinate from the first point as x 1 and then the y -coordinate from the second point as y 1 .

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