8-3: SlopeObjectives

The student will be able to:find the slope of a line given 2 points and

a graph.

First by rise/run then using the formula!

Find slope from tables.

What does the sign mean?

Where would you see this sign?

What does the 7% mean?

7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet

horizontally.

7%

So, what is slope???Slope is the steepness of a line.

7 feet

100 feet

Picking out type of slope.

• Flashcards PDF slides for examples.

• Using the whiteboards, I am going to show you 14 slides. You are to write the type of slope.

+, -, 0 (horizontal), or undefined (vertical)!

Let’s Review

• Draw the 4 types of slope:

1. 2. 3. 4.

Slope is the STEEPNESS of a LINE!

Slope can be expressed 4 different ways:

1. A line has a positive slope if it is going uphill from left to right.

2. A line has a negative slope if it isgoing downhill from left to right.

2 1

2 1

( ) vertical change

( ) horizontal change

y y risem

x x run

3.What is the slope of a horizontal line?

The line doesn’t rise!

m 0

number0

All horizontal lines have a slope of 0.

4. What is the slope of a vertical line?

The line doesn’t run!

All vertical lines have an undefined slope.

m number

0undefined

Warm-UP

• Everyone needs 2 colored pencils. For the NCTM activity worksheet “Just Slope”. Please following along.

Rise/Run

• Pay attention to the next few examples.

When given the graph, it is easier to apply “rise over run”.

Ex. 1)Determine the slope of the line.

Start with the lower point and count how much you rise and run to get to the other

point!

Determine the slope of the line.

6

3

run

3

6= =

1

2

rise

Notice the slope is positive AND the line increases!

Ex. 2) Determine the slope of the line.

The line is decreasing (slope is negative).

2

-1

rise

run

2

1 2

Find points on the graph. Use two of them and apply rise over run.

Remember…

Slope can be:

• Positive

• Negative

• 0/# = 0

• #/0 = Undefined

• Fractions, improper, 9/7, 11/9, 15/2, etc.

• Decimals ½ = 0.5, ¼ = 0.25, etc.

Let’s try more

• Using the colored pencils and the NCTM activity triangle worksheet, we will complete more rise/run problems.

• We will do some together then you will complete some on your own.

Who uses this stuff?

• Let’s think of several jobs that uses angles/slope/rate of change? (look at pdf)

1. roofer

Recall

1. Horizontal Lines have _________ slope.

2. Vertical Lines have ________ slope.

3. Draw the 4 types of slope AND label the slope

A. B. C. D.

m = m = m = m =

zero

undefined

Synonyms for slope?

1. angle

Slope, do we need a formula?

• You may not always be given a graph of the line to determine slope using rise/run. So we need another method.

• Using the slope formula, you can ALWAYS find slope if you know 2 points.

• Remember slope is a rate of change.

Change in y’s/ change in x’s

1) Find the slope of the line that passes through the points (-2, -2) and (4, 1).

(1 ( 2))

(4 ( 2))m

2 1

2 1

( )

( )

y ym

x x

(1 2)

(4 2)

When given points, it is easier to use the formula!

STEPS for using this formula:

1. LABEL your points- EVERYTIME!!!!!!!!

2. Plug in the formula and simplify the fraction.

13

6 2

Did you notice that Example #1 and Example #2 were the same problem

written differently?

(-2, -2) and (4, 1)6

31

2slope

You can do the problems either way!Which one do you think is easiest?

3) Find the slope of the line that goes through the points (-5, 3) and (-2, 1).

m y2 y1

x2 x1

m 1 3

2 ( 5)

m 1 3

2 5

m 2

3

Graphic Organizer

• Let’s use a graphic organizer to guide us for the method of finding slope using the formula.

• Remember HORIZONTAL lines =

• VERTICAL lines =

zero slope

Undefined slope

4) Find the slope of the line that passes through (3, 5) and (-1, 4).

Label the points:

A. 4

B. -4

C. ¼

D. - ¼

5) Determine the slope of the line shown.

A. -2 Could do this 2 ways!!

B. -½

C. ½

D. 2

What would be a real world ex? Think of a pool…

Practice, Whiteboards1. LABEL 2. plug in 3. simplify

• 1. (1, 1), (3, 4)

• 2. (0, 0), (5, 4)

• 3. (-2, 2), (-1, -2)

• 4. (7, -4), (9, -1)

• 5. (3, 5), (-2, 5)

• 6. (-1, 3), (-1, 0)

Review

• Handout with slope as a formula (partner slope activity). In partners of 2- here are the groups

• Please complete, check with a neighbor and turn in.

Collinear Points

• Lie on the same line.

• Points are collinear if they have the same slope.

Let’s Find Out• Are (3, 5), (4, 7) (7, 13) collinear?

• Calculate the slope the first two points: (3, 5) and (4, 7).

• Calculate the slope for the second pair of points (4, 7) and (7, 13).

• Yes.

You Try…

• Are (8, 9), (5, 3), and (2, -2) collinear?

• No.

1

Draw a line through the point (2,0) that has a slope of 3.

1. Graph the ordered pair (2, 0).

2. From (2, 0), apply rise over run (write 3 as a fraction).

3. Plot a point at this location.

4. Draw a straight line through the points.

3

The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.

To solve this, plug the given information into the formula

m

( y2 y

1)

(x2 x

1)

.

2 64

4 r

4 4

1 4 r

To solve for r, simplify and write as a proportion.

4 4

1 4 r

2 6

44 r

Cross multiply.

1(-4) = 4(4 – r)

Simplify and solve the equation.1(-4) = 4(4 – r)

-4 = 16 – 4r-16 -16

-20 = -4r-4 -45 = r

The ordered pairs are (5, 6) and (4, 2)