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

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Presentation transcript:

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

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

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

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

Vertical change = 14 P 2 (x 2, y 2 ) P 1 (x 1, y 1 ) Horizontal change = 7 Slope = vertical change horizontal change Slope = 14 or 2 7 Is the slope positive or negative? Positive

Find the slope of each line:

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) = undefined slope = ½

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

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 = 2Add 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 Graph y = 5x + 2 Graphing Equations

Graph 4x - 3y = 12 ● Solve for y first 4x - 3y =12Subtract 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. Graphing Equations

Graph y = x - 4 x y Graphing Equations

Find the value of r so that the line through (r, 6) (10, -3) has a slope of -3(10 – r) = 2(-9) r = -18 3r = 12 r = 4 Slope Formula Let (r, 6) = (x 1, y 1 ) and (10, -3) = (x 2, y 2 ) Subtract Cross Multiply Use the Distributive Property and simplify Add 30 to each side and simplify Divide each side by 3 and simplify 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 2. (r, -6) (5, -8); m = -8 r = 0 r = 4.75

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