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The slope of a non-vertical line is theratio of the vertical change (the rise) tothe horizontal change (the run) betweenany two points on the line. vertical change change in y = horizontal change change in x
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Example 1 Find the slope of the line shown.Write formula forslope. y2 – y1m= x2 – x1
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If you know any two points on a line, youcan find the slope of the line withoutgraphing. The slope of a line through thepoints (x1, y1) and (x2, y2) is as follows: rise y2 – y1 slope = = run x2 – x 1
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Example 1: Finding Slope, Given Two PointsFind the slope of the line that passes throughA. (–2, –3) and (4, 6).Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).y2 – y1 6 – (–3) Substitute 6 for y2, –3 for y1,x2 – x1 = 4 – (–2) 4 for x2, and –2 for x1. = 6 + 3 =9 4+2 6 =3 Simplify. 2 3The slope of the line is 2 .
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Example 2: Finding Slope, Given Two PointsFind the slope of the line that passes throughB. (1, 3) and (2, 1).Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).y2 – y1 1 – 3 Substitute 1 for y2, 3 for y1,x2 – x1 = 2 – 1 2 for x2, and 1 for x1. = −2 = –2 Simplify. 1The slope of the line that passes through(1, 3) and (2, 1) is –2.
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WARM UPFind the slope of the line that passes throughC. (3, –2) and (1, –2).Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).y2 – y1 –2 – (–2) Substitute −2 for y2, −2 for y1,x2 – x1 = 1 – 3 1 for x2, and 3 for x1. = −2 + 2 Rewrite subtraction as addition of 1–3 the opposite. 0 = –2 = 0The slope of the line that passes through(3, –2) and (1, –2) is 0.
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WARM UPFind the slope of the line that passes throughA. (3, 5) and (3, 1).Let (x1, y1) be (3, 5) and (x2, y2) be (3, 1).
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Helpful HintYou can use any two points to find theslope of the line.The slope of a line may be positive, negative,zero, or undefined. You can tell which of theseis the case by looking at the graphs of a line—you do not need to calculate the slope.
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