Calculating slope from a graph
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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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Slope

Calculating slope from a graph

Slope

Click mouse to play movie

Becky Afghani, LBUSD Math Curriculum Office, 2003


How steep is the steepest roller coaster

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

How steep is the steepest roller coaster?


Objective

Objective

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


Why are we learning this

Why are we learning this?

  • You will use slope to graph a line without having to use a T-table

  • Knowing slope is a 7th grade standard:

    • AF 3.3: Graph linear functions, noting that the vertical change per unit of horizontal change is always the same and know that the ratio (“rise over run”) is called the slope of a graph.

  • There are 2 items on the CAHSEE relating to slope.

Becky Afghani, LBUSD Math Curriculum Office, 2003


Imagine a roller coaster moving from left to right

Imagine a roller coaster moving from LEFT to RIGHT

Becky Afghani, LBUSD Math Curriculum Office, 2003


There are four different kinds of slope the coaster could encounter

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

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Positive

Slope

Uphill

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Negative

Slope

Downhill

Becky Afghani, LBUSD Math Curriculum Office, 2003


And 2 special cases

And 2 Special Cases…

The impossibly scary coaster

The zero-fun coaster

What kind of slope are they?

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Zero

Slope

Horizontal

Aw!

That’s zero fun!

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Undefined

Slope

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

Vertical

Becky Afghani, LBUSD Math Curriculum Office, 2003


What are the 4 types of slope

A

B

What are the 4 types of slope?

  • Determine who will be shoulder-partner A and shoulder-partner B

  • A says the name of a type of slope

  • B describes what it looks like

  • Name and describe all four types of slope

One type of slope is…

That one is…

Becky Afghani, LBUSD Math Curriculum Office, 2003


For the following slides call out whether the slope is positive negative zero or undefined

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!

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

1

2

3

negative

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

1

2

3

positive

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

1

2

3

zero

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

1

2

3

undefined

Becky Afghani, LBUSD Math Curriculum Office, 2003


How can you describe the steep ness of a roller coaster

How can you describe the steepness of a roller coaster?

  • Slopeis a number which describes the steepness of a line.

  • We use the variable m to stand for slope.

Dude, why’d you use the letter m?

I named it after my Mom

Becky Afghani, LBUSD Math Curriculum Office, 2003


What is slope

A

B

What is slope?

  • Determine who will be shoulder-partner A and shoulder-partner B

  • A describes what slope is

  • B tells what letter is used for slope

Slope is…

We use the letter…

Becky Afghani, LBUSD Math Curriculum Office, 2003


What do big slopes and small slopes look like

What do big slopes and small slopes look like?

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

Slope is positive one

m = 1

45

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Slope is greater than positive one

m = 3

Steep climb for a coaster

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Slope is between zero and one

m = 1/4

Shallow climb for a coaster

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Slope is negative one

m = -1

45

Same as positive one, just downhill

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

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


Slope

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


Let s see if you can remember

Let’s see if you can remember…

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


Slope

Do you remember?

m = 1

m = 8

m = -1

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Do you remember?

m = 1

m = 4

m = 1/4

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Do you remember?

m = 1

m = 3

m = 1/3

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Do you remember?

m = -1

m = 1

m = -4

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Do you remember?

m = -1

m = -3

m = -1/3

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Do you remember?

m = -1

m < -4

m = -1/4

Becky Afghani, LBUSD Math Curriculum Office, 2003


Now let s practice

Now, let’s practice…

  • You will be given a slope.

  • Make the line with your arms.

  • Think… Positive or Negative

  • Then… Steep, Shallow or 45-degree

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m = 1

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m = -1

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m = 3

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m < -3

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m = 1/4

Becky Afghani, LBUSD Math Curriculum Office, 2003


Slope

Stand up and show me with your arms – wait for my signal

m = -1/4

Becky Afghani, LBUSD Math Curriculum Office, 2003


How do you calculate the slope of a line

How do you calculate the slope of a line?

  • Pick two points on the line

  • Calculate “rise over run”

  • Determine the sign

There are 3 steps:

Becky Afghani, LBUSD Math Curriculum Office, 2003


Start with 2 points on gridline intersections

Not OK

Not OK

Not OK

OK

OK

OK

OK

OK

OK

OK

OK

Step 1

Start with 2 points on gridline intersections

(2, 3)

(1, 1)

(0, -1)

(-1, -3)


How do you calculate the slope of a line1

Step 2

Run = 1

Rise = 2

How do you calculate the slope of a line?

Vertical change

m

Slope =

divided by

Horizontal change

Rise

m

OR...

Slope =

divided by

Run

Becky Afghani, LBUSD Math Curriculum Office, 2003


What sign is it

Step 3

Show me!

What sign is it?

Look to see if the slope is increasing

Positive

Or decreasing

Negative

Becky Afghani, LBUSD Math Curriculum Office, 2003


Step 1 choose 2 points

Step 2:

Rise

Slope =

divided by

Run

2

1

Rise

divided by

Run

Model # 1: Watch me do the three steps

Step 1: Choose 2 points

Run = 1

positive

Rise = 2

Step 3:

Determine

the sign

m = 2

+


Step 1 choose 2 points1

Step 2:

Rise

Slope =

divided by

Run

1

3

Rise

divided by

Run

Model # 2: Watch me do the three steps

Step 1: Choose 2 points

Run = 3

Rise = 1

negative

Step 3:

Determine

the sign

m = 1/3

-


With your partner

Rise Over Run

Choose Two points

Determine Sign

With your partner…

  • Put these three steps in the correct order.

  • I will choose a student at random to share out.

Becky Afghani, LBUSD Math Curriculum Office, 2003


Practice 1 find the slope of this line

Rise

divided by

Think Pair Share

Run

Rise = 3

Run = 2

Practice # 1: Find the slope of this line

+

Step 1: Choose Two points

Step 2: Rise Over Run

Step 3: Determine Sign


Practice 2 find the slope of this line

Rise

divided by

Think Pair Share

Run

Run = 3

Rise = 1

Practice # 2: Find the slope of this line

negative

Step 1: Choose Two points

Step 2: Rise Over Run

Step 3: Determine Sign


Practice 3 find the slope of this line

Think Pair Share

Rise = 2

Run = 5

Practice # 3: Find the slope of this line

+

Step 1: Choose Two points

Step 2: Rise Over Run

Step 3: Determine Sign


Practice 4 find the slope of this line

Rise

divided by

Think Pair Share

Run

Run = 2

Rise = 3

Practice # 4: Find the slope of this line

negative

Step 1: Choose Two points

Step 2: Rise Over Run

Step 3: Determine Sign


Before you leave

Before you leave:

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, 45-degree angle…)

3. What is the slope of the line above?

Becky Afghani, LBUSD Math Curriculum Office, 2003


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