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Unit 5.5

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Unit 5.5

1. 1. Unit 5.5Find Slope and Rate of Change
2. 2. 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
3. 3. Example 1 Find the slope of the line shown.Write formula forslope. y2 – y1m= x2 – x1
4. 4. 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
5. 5. 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 .
6. 6. 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.
7. 7. 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.
8. 8. 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).
9. 9. 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.