rate of change and calculation verbal presentation https://www.youtube.com/watch?v=lWRhQHb1dtY https://www.facebook.com/secondarymathandscience/

1. Topic 4) Rate of Change
and Slope

2. The rate of change of a function is a
ratios that compares the difference
between two output values to the
difference between the corresponding
input values.

3. The Magnum
Cedar Point, OH
Ghost Rider
Knott’s Berry Farm Xcelerator
Knott’s Berry Farm
Superman
6 Flags Magic
Mountain
Son of Beast
King’s Island, OH
How steep is the steepest roller coaster?
These are
completely
vertical!

4. Imagine a roller coaster moving
from LEFT to RIGHT

5. There are four different kinds of slope
the coaster could encounter...

8. And 2 Special Cases…
The zero-fun
coaster
The
impossibly
scary
coaster
What
kind of
slope are
they?

9. Aw!
That’s
zero fun!

10. That’s a really
scary coaster,
so the slope
is…

11. For the following slides,
call out whether the slope is positive,
negative, zero, or undefined.
Wait for the count of 3
before you say your answer!

16. How do you calculate the slope
of a line?
1. Pick two points on the line
2. Calculate “rise over run”
3. Determine the sign

17. Start with 2 points on gridline
intersections

18. How do you calculate the slope of a
line?
Slope =
Vertical change
Horizontal change
OR...
Rise
Run
m
Slope =m Rise
Run

19. What sign is it?
Look to see if the slope is
increasing
Or decreasing

20. Model # 1: Watch me do the
three steps
Step 1: Choose 2 points
Rise = 2
Run = 1
Rise
Run
2
1
m = 2
Step 3:
Determine
the sign
Slope =
Rise
Run
Step 2:
+

21. Model # 2: Watch me do the
three steps
Step 1: Choose 2 points
Rise = 1
Run = 3
Rise
Run
1
3
m = 1/3
Step 3:
Determine
the sign
Slope =
Rise
Run
Step 2:
-

22. Practice # 3: Find the slope of this line
Rise
Run
Rise = 3
Run = 2
2
3
m
+

23. Practice # 4: Find the slope of this line
Rise = 1
Run = 3
3
1
m
Rise
Run

24. Quick Preview
The diagram at the right shows the
side view of a ski lift.
1. What is the vertical change from:
a. A to B?
b. B to C?
c. C to D?
2. What is the horizontal change from:
a. A to B?
b. B to C?
c. C to D
3. Find the ratio of the vertical change to the
horizontal change for each section of the ski
lift.
4. Which section is the steepest?
10 feet
40 feet
10 feet
30 feet
30 feet
30 feet A 1 B 4 C 1
B 3 C 3 D 3
= ; = ; =
B to C

25. Slope Formula
12
12
xx
yy
m



5. Given (5, -3) and (-4, 2), find
the slope of the line.
x1 y1 x2 y2
m =
54
)3(2


9
5



26. Slope Formula
12
12
xx
yy
m



6. Given (0, -2) and (4, -2), find
the slope of the line.
x1 y1 x2 y2
m =
04
)2(2


4
0
 0

27. Wrap Up Rate of Change (includes units)
 Slope
 Positive
 Negative
 Zero
 Undefined
run
rise 
12
12
xx
yy
m




28. Additional Example 2: Driving Application
The table shows the driving distances that Jesse
recorded.
A. Determine whether the rates of change are
constant or variable.
The rate of change is constant.

29. Additional Example 2: Driving Application
B. Graph the data and connect the points with
line segments. If the rate of change is constant,
find and interpret the slope.
The slope is . This means he drove 3 mi. every 5 min.
3
5
The rate of change between
any two points is . The
slope of the line is .3
5
3
5

30. Check It Out: Example 2
The table shows the driving distances that Barry
recorded.
Determine whether the rates of change are
constant or variable.
The rates of change are variable.
3
1
= 3 6
3
= 2 12
6
= 2 18
9
= 2
Time (min) 1 3 6 9 12
Distance
(miles)
3 6 12 18 24
24
12
= 2

31. Non-Linear Function
non-linear functions, the "average rate of change"
is not constant.

32. For more example and discussion
https://www.facebook.com/secondarymathandscience/
For verbal presentation
https://www.youtube.com/watch?v=lWRhQHb1dtY