Calculating slope from a graph. Slope. Click mouse to play movie. The Magnum Cedar Point, OH. Superman 6 Flags Magic Mountain. Ghost Rider Knott’s Berry Farm. Xcelerator Knott’s Berry Farm. These are completely vertical!. Son of Beast King’s Island, OH.
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Calculating slope from a graph
Slope
Click mouse to play movie
Becky Afghani, LBUSD Math Curriculum Office, 2003
The Magnum
Cedar Point, OH
Superman
6 Flags Magic Mountain
Ghost Rider
Knott’s Berry Farm
Xcelerator
Knott’s Berry Farm
These are
completely
vertical!
Son of Beast
King’s Island, OH
Given a graph of a line, you will calculate the slope of the line.
How
steep is it?
Becky Afghani, LBUSD Math Curriculum Office, 2003
Becky Afghani, LBUSD Math Curriculum Office, 2003
Becky Afghani, LBUSD Math Curriculum Office, 2003
Becky Afghani, LBUSD Math Curriculum Office, 2003
Positive
Slope
Uphill
Becky Afghani, LBUSD Math Curriculum Office, 2003
Negative
Slope
Downhill
Becky Afghani, LBUSD Math Curriculum Office, 2003
The impossibly scary coaster
The zerofun coaster
What kind of slope are they?
Becky Afghani, LBUSD Math Curriculum Office, 2003
Zero
Slope
Horizontal
Aw!
That’s zero fun!
Becky Afghani, LBUSD Math Curriculum Office, 2003
Undefined
Slope
That’s a really scary coaster, so the slope is…
Vertical
Becky Afghani, LBUSD Math Curriculum Office, 2003
A
B
One type of slope is…
That one is…
Becky Afghani, LBUSD Math Curriculum Office, 2003
Wait for the count of 3 before you say your answer!
Becky Afghani, LBUSD Math Curriculum Office, 2003
1
2
3
negative
Becky Afghani, LBUSD Math Curriculum Office, 2003
1
2
3
positive
Becky Afghani, LBUSD Math Curriculum Office, 2003
1
2
3
zero
Becky Afghani, LBUSD Math Curriculum Office, 2003
1
2
3
undefined
Becky Afghani, LBUSD Math Curriculum Office, 2003
Dude, why’d you use the letter m?
I named it after my Mom
Becky Afghani, LBUSD Math Curriculum Office, 2003
A
B
Slope is…
We use the letter…
Becky Afghani, LBUSD Math Curriculum Office, 2003
When the slope is positive…
m = 1 is a 45 degree angle
m > 1 is a steep line
0 < m < 1 is a shallow line
Negatives are the same but downhill…
Show me!
Becky Afghani, LBUSD Math Curriculum Office, 2003
Slope is positive one
m = 1
45
Becky Afghani, LBUSD Math Curriculum Office, 2003
Slope is greater than positive one
m = 3
Steep climb for a coaster
Becky Afghani, LBUSD Math Curriculum Office, 2003
Slope is between zero and one
m = 1/4
Shallow climb for a coaster
Becky Afghani, LBUSD Math Curriculum Office, 2003
Slope is negative one
m = 1
45
Same as positive one, just downhill
Becky Afghani, LBUSD Math Curriculum Office, 2003
Slope is less than negative one
Steep drop for a coaster
m = 3
These are “big” negative numbers
Becky Afghani, LBUSD Math Curriculum Office, 2003
These are “small” negative numbers
m = 1/4
Shallow drop for a coaster
Slope is between negative one and zero
Becky Afghani, LBUSD Math Curriculum Office, 2003
You will see a graph and some choices.
Use what you know about steep and shallow lines to pick the only possible slope.
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m = 8
m = 1
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m = 4
m = 1/4
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m = 3
m = 1/3
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m = 1
m = 4
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m = 3
m = 1/3
Becky Afghani, LBUSD Math Curriculum Office, 2003
Do you remember?
m = 1
m < 4
m = 1/4
Becky Afghani, LBUSD Math Curriculum Office, 2003
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m = 1
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m = 1
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m = 3
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m < 3
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m = 1/4
Becky Afghani, LBUSD Math Curriculum Office, 2003
Stand up and show me with your arms – wait for my signal
m = 1/4
Becky Afghani, LBUSD Math Curriculum Office, 2003
There are 3 steps:
Becky Afghani, LBUSD Math Curriculum Office, 2003
Not OK
Not OK
Not OK
OK
OK
OK
OK
OK
OK
OK
OK
Step 1
(2, 3)
(1, 1)
(0, 1)
(1, 3)
Step 2
Run = 1
Rise = 2
Vertical change
m
Slope =
divided by
Horizontal change
Rise
m
OR...
Slope =
divided by
Run
Becky Afghani, LBUSD Math Curriculum Office, 2003
Step 3
Show me!
Look to see if the slope is increasing
Positive
Or decreasing
Negative
Becky Afghani, LBUSD Math Curriculum Office, 2003
Step 2:
Rise
Slope =
divided by
Run
2
1
Rise
divided by
Run
Model # 1: Watch me do the three steps
Run = 1
positive
Rise = 2
Step 3:
Determine
the sign
m = 2
+
Step 2:
Rise
Slope =
divided by
Run
1
3
Rise
divided by
Run
Model # 2: Watch me do the three steps
Run = 3
Rise = 1
negative
Step 3:
Determine
the sign
m = 1/3

Rise Over Run
Choose Two points
Determine Sign
Becky Afghani, LBUSD Math Curriculum Office, 2003
Rise
divided by
Think Pair Share
Run
Rise = 3
Run = 2
+
Step 1: Choose Two points
Step 2: Rise Over Run
Step 3: Determine Sign
Rise
divided by
Think Pair Share
Run
Run = 3
Rise = 1
negative
Step 1: Choose Two points
Step 2: Rise Over Run
Step 3: Determine Sign
Think Pair Share
Rise = 2
Run = 5
+
Step 1: Choose Two points
Step 2: Rise Over Run
Step 3: Determine Sign
Rise
divided by
Think Pair Share
Run
Run = 2
Rise = 3
negative
Step 1: Choose Two points
Step 2: Rise Over Run
Step 3: Determine Sign
1. What type of slope is shown? (Positive, negative, zero or undefined?)
2. What would a slope of 1/2 look like? (Uphill, downhill, steep, shallow, 45degree angle…)
3. What is the slope of the line above?
Becky Afghani, LBUSD Math Curriculum Office, 2003