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Algebra Lesson 6-1 Created by Jeff M. Downs

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Important Vocabulary Terms The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line. You can describe steepness by using slope of a line.

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The Slope Ratio horizontal run = 5 vertical rise = 10 slope = vertical rise horizontal run so slope = 10 5 = 2 1 = 2 Remember to always simplify the ratio.

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Let’s Try It Out! horizontal run = 200 ft vertical rise = 40 ft Let’s try and find the slope of a hill that has a vertical rise of 40ft and a horizontal run of 200ft. Let m represent the slope. Don’t touch that button unless you have tried it on your own first! S Click the green solution button to check your own work

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Apply the formula- vertical rise to horizontal run Vertical rise = 40 ft Horizontal run = 200 ft 40 ft. 200 ft. 40 Find the GCF = 1 5 The slope of the hill is 1 5 backforward

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1 3 5 7 y 1357.. USING A COORDINATE PLANE TO FIND SLOPE The coordinates are (2,2) and (6,5) Use the formula: rise run = 5 - 2 6 - 2 = 3 4

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.. (x 2, y 2 ) (x 1, y 1 ) x 2 - x 1 y 2 - y 1 The slope m of a line that passes through the points (x 1, y 1 ) and (x 2, y 2 ) is m = rise run = change in y change in x = y 2 - y 1 x 2 - x 1 The Slope Of A Line

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1. Positive Slope 2. Negative Slope 3. Zero Slope 4. Undefined Slope A line that rises from left to right A line falls from left to right A line is horizontal The line is vertical *Continue to click mouse for information*

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It’s your turn: Use a piece of graph paper to help you illustrate the slope (x, y ) 11 = (1,0) and (x, y ) = (3, 4) 2 2 (x, y ) 11 = (0, 9) and (x, y ) = (4, 7) 2 2 (x, y ) 11 = (1, 2) and (x, y ) = (5, 2) 2 2

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1 3 5 7 y 1357. (x, y ) 11 = (1, 0) and (x, y ) = (3, 4) 2 2 m = y 2 y 1 - x 2 x 1 - 4 - 0 3 - 1 m = 4 2. The slope of the line is 2

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1 3 5 7 y 1357. m = y 2 y 1 - x 2 x 1 - 7 - 9 4 - 0. (x, y ) 11 = (0, 9) and (x, y ) = (4, 7) 2 2 The slope of the line is -1 which makes it a negative slope. 2 m = -2 4 or 2

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(x, y ) 11 = (1, 2) and (x, y ) = (5, 2) 2 2 1 3 5 7 y 1357 m = y 2 y 1 - x 2 x 1 - 2 - 2 5 - 1 The slope of the line is zero which makes it a zero slope. m = 0 4 or0..

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Let’s Review Slope is the steepness of a line It is described by a ratio of rise to run A coordinate plane can be used to find the slope of a line There are 4 types of slope –positive slope –negative slope –zero slope –undefined slope

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