Slope or Rates of Change

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Presentation transcript:

Slope or Rates of Change Lesson 5-1 Slope or Rates of Change

Click the mouse button or press the Space Bar to display the answers. Transparency 1

Transparency 1a

Objectives Find the slope of a line Use rate of change to solve problems

Vocabulary Slope – The ratio of the change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) as you move from one point to another along a line Rate of change – How a quantity is changing over time

x-y Coordinate Plane Point Plotting Slope, m (∆y / ∆x) 5 m = ------ -3 up 7 left 4 right 5 ∆y = 15 rise down 8 run ∆x = -9 (x, y) (-4, 7) (5, -8) x – left or right y – up or down (x, y) (-4, 7) (5, -8) rise: ∆y – change in y (7 - -8 = 15) run: ∆x – change in x (-4 – 5 = -9)

Example 1 Find the slope of the line that passes through (–3, 2) and (5, 5). Let and Substitute. Simplify. Answer: The slope is

Example 2 Find the slope of the line that passes through (–3, –4) and (–2, –8). Let and Substitute. Simplify. Answer: The slope is –4.

Example 3 Find the slope of the line that passes through (–3, 4) and (4, 4). Let and Substitute. Simplify. Answer: The slope is 0. (A horizontal line!)

Example 4 Find the slope of the line that passes through (–2, –4) and (–2, 3). Let and Answer: Since division by zero is undefined, the slope is undefined. (A vertical line!)

Example 5 Find the value of r so that the line through (6, 3) and (r, 2) has a slope of ½ Slope formula Substitute. Subtract. Find the cross products. Simplify. Answer: Simplify.

Example 6 Travel The graph to the right shows the number of U.S. passports issued in 1991, 1995, and 1999. Find the rates of change for 1991-1995 and 1995-1999. Use the formula for slope. millions of passports years

Example 6 cont 1991-1995: Substitute. Simplify. Answer: The number of passports issued increased by 1.9 million in a 4-year period for a rate of change of 475,000 per year.

Example 6 cont 1995-1999: Substitute. Simplify. Answer: Over this 4-year period, the number of U.S. passports issued increased by 1.4 million for a rate of change of 350,000 per year.

Summary & Homework Summary: Homework: The slope of a nonvertical line is the ratio of the rise (the change in y) to the run (the change in x). Homework: Pg. 260 16-46 even Pg. 831 1-13 all