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Published byEdward Maggart Modified over 2 years ago

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SLOPE 2.13.12 Objectives: Find the slope of a line given the coordinates of two points on the line Graph equations using y=mx+b form.

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What is Slope? - SLOPE - + SLOPE + + SLOPE + Steepness Rise Run Change in Y Change in X Amount of Slant Y=mx + b

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The Graph of y = mx +b Consider the graph of y = x - 2 5432154321 -2 -3 -4 -5 y -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x Compare to the graph of y = ½x - 2 Compare to the graph of y=2x-2

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The Graph of y = mx +b Consider the graph of y = x - 2 5432154321 -2 -3 -4 -5 y -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x Compare to the graph of y = -1x - 2 Compare to the graph of y = -2x - 2

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Determining Slope Rise=1 Slope= 1212 Slope=3 Rise=6 Run =2 Rise=12 Run =4

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Determining Slope Run = -4 Rise= -2 Slope= -2 Slope= 0 Run = 1 Rise= 0 Run = n Rise= 8 = -2 1

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Determining Slope The Slope is UNDEFINED Rise= n Run = 0

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Determining Slope (-4, -6) (2, 5) Pick 2 points on the line Find the change in the Y- coordinates by subtracting(rise) Find the change in the X- coordinates by subtracting(run) Write as a ratio ( rise / run ) 5-(-6) 2-(-4) = 11 6

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Determining Slope (x 2, y 2 ) (x 1, y 1 ) In general, to find the slope given two points on a line: Subtract the Y-coordinates (rise) Subtract the X-coordinates (run) Write as a ratio ( rise / run ) Y 2 -Y 1 X 2 -X 1 m = Y 1 -Y 2 X 1 -X 2 =

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Slope Summary Slope = 0 Positive Slope Negative Slope Negative slope is a downer Undefined Slope

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Linear Equations (y = mx + b) b = y-intercept plot (0,b) to get your first point m = slope written as a fraction slope = rise / run Lean up and to the right if positive Lean down and to the right if negative

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