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Rate of Change and Slope

Rate of Change and Slope. Objectives: • Use the rate of change to solve problems. • Find the slope of a line. Slope. The word slope (gradient, incline, pitch) is used to describe the measurement of the steepness of a straight line.

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Rate of Change and Slope

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  1. Rate of Change and Slope Objectives: • Use the rate of change to solve problems. • Find the slope of a line.

  2. Slope The word slope (gradient, incline, pitch)is used to describe the measurement of the steepness of a straight line. The slope of a line is also known as the rate of change.

  3. Types of Slopes Negative Slope m = - Positive Slope m = + Undefined Slope Zero Slope m = 0

  4. Slope is a ratio and can be expressed as: Slope = Vertical Change or Rise or Horizontal ChangeRun To find the slope in this lesson you must use…. Slope formula

  5. Is the slope positive or negative? Positive P2(x2, y2) Slope = vertical change horizontal change Vertical change = 14 Slope = 14 or 2 7 P1(x1, y1) Horizontal change = 7

  6. Find the slope of each line:

  7. Practice Find the slope of the line that passes through (-1, 4) and (1, -2). Then graph the line.

  8. Find the slope of the line that passes through each pair of points. 1. (7, 6), (7, 4) 2. (9, 3), (7, 2) = ½ =undefined slope

  9. Find the slope of the line that passes through each pair of points. 3. (1, 2) (-1, 2) 4. (9, -4) (7, -1) slope = 0 slope =

  10. Graph on the coordinate plane • m= -3 • Passes through (-1, 2)

  11. Graph on the coordinate plane • m= 1/2 • Passes through (2, 3)

  12. Graph on the coordinate plane • m= undefined • Passes through (3, 1)

  13. Graphing Equations • Example: Graph the equation -5x + y = 2 Solve for y first. -5x + y = 2 Add 5x to both sides y = 5x + 2 • The equation y = 5x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

  14. x y Graphing Equations Graph y = 5x + 2

  15. Graph 4x - 3y = 12 Graphing Equations • Solve for y first 4x - 3y =12 Subtract 4x from both sides -3y = -4x + 12 Divide by -3 y = x + Simplify y = x – 4 • The equation y = x - 4 is in slope-intercept form, y=mx+b. The y -intercept is -4 and the slope is . Graph the line on the coordinate plane.

  16. x y Graphing Equations Graph y = x - 4

  17. Find the value of r so that the line through (r, 6) (10, -3) has a slope of Slope Formula Let (r, 6) = (x1, y1) and (10, -3) = (x2, y2) Subtract -3(10 – r) = 2(-9) Cross Multiply -30 + 3r = -18 Use the Distributive Property and simplify 3r = 12 Add 30 to each side and simplify Divide each side by 3 and simplify r = 4 The line goes through (4, 6)

  18. Find the value of r so the line that passes through each pair of points has the given slope. 1. (1, 4) (-1, r); m = 2 r = 0 2. (r, -6) (5, -8); m = -8 r = 4.75

  19. Questions . . . ? Comments . . . ? Concerns . . . ?

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