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SLOPE 2.13.12

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. + SLOPE +. - SLOPE -. Rise Run. Y=mx + b. Amount of Slant. y. 5 4 3 2 1. x.

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SLOPE 2.13.12

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  1. 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.

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

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

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

  5. Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 1 2 Slope= Slope=3

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

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

  8. Determining Slope • 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)

  9. Determining Slope • 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

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

  11. 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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