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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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.

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

The Graph of y = mx +b Consider the graph of y = x - 2 y 5 4 3 2 1 -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

The Graph of y = mx +b Consider the graph of y = x - 2 y 5 4 3 2 1 -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

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

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

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

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

Determining Slope Y1-Y2 Y2-Y1 m = X1-X2 X2-X1 In general, to find the slope given two points on a line: Subtract the Y-coordinates (rise) (x1, y1) Subtract the X-coordinates (run) Write as a ratio (rise/run) (x2, y2) Y1-Y2 X1-X2 Y2-Y1 m = = X2-X1

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

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