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The Slope Of A Line Objective: To find the slope of a line and to graph a line given its slope and a point.

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What is slope? There are several definitions, but they are all related. Rate of change

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Example y x Distance in miles Time In hours (x 1,y 1 ) (x 2,y 2 ) run = x 1 – x 2 rise = y 1 – y 2 m = rise/run = (y 1 – y 2 )/(x 1 – x 2 ) = miles/hour

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Find the slope between the two points (2, 4) and (5, 1) (-3, 1) and (6, 4) (2, 3) and (-1, 3) (-2, 5) and (-2, 7) m = -1 m = 1/3 m = 0 No slope or undefined slope

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Theorem The slope of a line in standard form Ax + By = C is -A/B

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Point Slope Form y – y 1 = m(x – x 1 ) Variation: y = y 1 + (x – x 1 )m

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Graph The Line Passing Through (1,2) with a slope m = ¼ Start by graphing the point (1,2) Since slope is rise over run move up 1 unit and right 4 units -4 -3 -2 -1 43214321 1 2 3 4 5 6 -2 -3 -4

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Rate of Change and Slope Monday, November 1, 2010.

Rate of Change and Slope Monday, November 1, 2010.

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