610 likes | 1.54k Views
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.
E N D
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. The slope of a line is also known as the rate of change.
Types of Slopes Negative Slope m = - Positive Slope m = + Undefined Slope Zero Slope m = 0
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
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
Practice Find the slope of the line that passes through (-1, 4) and (1, -2). Then graph the line.
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
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 =
Graph on the coordinate plane • m= -3 • Passes through (-1, 2)
Graph on the coordinate plane • m= 1/2 • Passes through (2, 3)
Graph on the coordinate plane • m= undefined • Passes through (3, 1)
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.
x y Graphing Equations Graph y = 5x + 2
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.
x y Graphing Equations Graph y = x - 4
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)
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
Questions . . . ? Comments . . . ? Concerns . . . ?