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

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Transparency 1

3. Transparency 1a

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

5. 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

6. 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 ( = 15)
run: ∆x – change in x (-4 – 5 = -9)

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

8. 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.

9. 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!)

10. 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!)

11. 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.

12. 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 and
Use the formula for slope.
millions of passports
years

13. 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.

14. 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.

15. 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 even
Pg all