the slope “rate of change”. the rate of change slope = 0 no rate of change rise = 0, run =...
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The Slope
“Rate of Change”
The Rate of Change
Slope = 0
No rate of change
Rise = 0, Run = (whatever)
Flat Surface
Yawn!!Zzzz...
No (zero) Slope = No Rate of Change
I might want to move…
Small Slope = Slow Rate of Change
Slope = 1/3
Small rate of change
Rise = 1, Run = 3
Slight Downhill
Slope = 5
Bigger rate of change
Rise = 10, Run = 2
Steep Downhill
YIKES!!RUN!!
HAHA!
Large Slope = Fast Rate of Change
Infinite (∞) Slope =
No Rate of Change
The Slope never touches the ball, so it has no affect on the ball.
No affect means no rate of change.
It’s called “Undefined”
Looks like a cliff
RecapNo (Zero) Slope = No Rate of Change
Small Slope = Slow Rate of Change
Large Slope = Fast Rate of Change
Infinite (∞) Slope = “Undefined” (No Effect)
Slope = 0 Slope = ⅓ Slope = 5 Slope = ∞
No Change Smaller Change Bigger Change Undefined Change
Flat Surface Slight Downhill
(or Uphill)
Steep Downhill
(or Uphill)
A Cliff
Rise = 0 = Flat Surface
Usually when Rise < Run
Usually when Rise > Run
Run = 0 = Cliff
Uphill or Downhill?
• Positive Slopes are UPHILL
• Negative Slopes are DOWNHILL
Slope
Describe the next few slope values as:
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Small Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Click on the Correct Answer)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Rise = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Rise > Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes Smaller Change
c) Steep Up/Downhill, Large Slopes Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Run = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Notice how Rise < Run)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Click on the Correct Answer)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Rise = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes Smaller Change
c) Steep Up/Downhill, Large Slopes Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Run = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is Rise < Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Notice how Rise > Run)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Click on the Correct Answer)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Rise > Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes Smaller Change
c) Steep Up/Downhill, Large Slopes Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Run = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is Rise < Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Notice how Rise = 0)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Click on the Correct Answer)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is the Rise > Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is Rise < Run?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes, Smaller Change
c) Steep Up/Downhill, Large Slopes, Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Is Rise = 0?)
Questions (Part I)
a) Flat Surface, Zero Slope, No Change
b) Slight Up/Downhill, Small Slopes Smaller Change
c) Steep Up/Downhill, Large Slopes Bigger Change
d) Cliff, ∞ slope, Undefined Change
(Notice how the Run = 0)
Questions (Part II)
Identify each of the following slope values as either:
a)Going Uphill (U)
Or
b) Going Downhill (D)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
Is the slope positive or negative?(click on “doh” to try again)
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
Is the slope positive or negative?(Click on “doh” to try again)
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
DIs the slope positive or negative?(Click on “doh” to try again)
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
Is the slope positive or negative?(Click on “doh” to try again)
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
Is the slope positive or negative?(Click on “doh” to try again)
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
DIs the slope positive or negative?(Click on “doh” to try again)
1)
2)
3)
4)
5)
6)
Select (U)phill or (D)ownhill
U
D
U
D
U
D
U
D
U
D
U
D
1)
2)
3)
4)
5)
6)
In Conclusion
• Bigger Numbers = Steeper Slopes (Bigger Change)
• Zero Slope = Flat Line (No Change)
• Infinite Slope = Cliff (Undefined Change)
• Positive Slope = Uphill
• Negative Slope = Downhill
Homework