Finding The Slope of a Line

What is the meaning of this sign?

1. Icy Road Ahead2. Steep Road Ahead3. Curvy Road Ahead4. Trucks Entering

Highway Ahead

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 feetJust copy this definition

Slope can be expressed different ways:

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

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

2 1

2 1

( ) vertical change( ) horizontal changey y risemx x run

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Finding the slope of a line

on a graph

Graph (3, 2) and (-1, -1)

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Draw a line through the points.

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Now that we have our line lets find its slope.

Remember we are finding the following ratio:

Vertical or Rise Horizontal Run

Just read

VERTICAL Changeor the RISE

3

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HORIZONTAL Changeor the RUN

4

3

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Vertical Rise Horizontal Run

34

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

Determine the slope of the line.Just watch

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

run36

= =12

rise

Notice the slope is positive AND the line increases!

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Determine the slope of the line shown.

1. -22. -½3. ½4. 2

If there are no points on the graph place points on the line at an intersection.

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Determine the slope of the line shown.

1. -22. -½3. ½4. 2

If there are no points on the graph place points on the line at an intersection.

2

-1

RiseRun

2-1

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Find the slope of these lines

What is the slope of a horizontal line?

The line doesn’t rise!

m 0

number0

All horizontal lines have a slope of 0.

What is the slope of a vertical line?

The line doesn’t run!

All vertical lines have an undefined slope.

m number

0undefined

Remember the word “VUXHOY”

Vertical linesUndefined slopeX = number; This is the equation of the line.Horizontal linesO - zero is the slopeY = number; This is the equation of the line.

Copy in notebook

Record notes in foldable first under the GRAPH heading.

Partner Work – Pass out worksheet. Find the slopes of the graphs.

Go ahead on slides for finding slopes other ways.

Finding the slope of a line

when given two points

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 ymx x

(1 2)(4 2)

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

Label your points.

136 2

y1y2x1

x2

m represents slope

Take Notes!

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

written differently?

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

312

slope

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

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

m y2 y1

x2 x1

1 32 ( 5)

m

1 32 5

m

27

m

y2y1 x2x1

Write formula

Label points

Substitute number for variables.

Take Notes!

Find the slope of the line that passes through (2, 5) and (3, 6).

1. 22. 13. - 14. -2

1st – Write Formula for finding slope2nd – Label your points3rd – Substitute numbers in for variables.4th – Simplify.

Do in notebook!

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

1. 02. 83. - 84. -1/8

Do in Notebook!

Find the slope of the line that passes through (4, 1) and (-6, -4).

1. 22. -23. -1/24. 1/2

Do in Notebook!

Find the slope of the line that passes through (-2, 4) and (10, 0).

1. 1/32. -1/33. -1/24. 1/2

Do in Notebook!

Find the slope of the line that passes through (3, 2) and (3, -2).

1. 02. 43. -44. undefined

Do in Notebook!

Find the slope of the line that passes through (2, 7) and (-2, -3).

1. 5/22. -5/23. -44. 0

Do in Notebook!

Record notes in foldable first under Ordered Pairs heading.

Activity– Pass out worksheet. Find the slopes of the graphs.

Go ahead on slides for finding slopes other ways.

Finding the slope of a line from a table

Calculate slope from a table.X Y

1 10

2 20

3 30

4 40

5 50

Is this function linear?Calculate slope from a table.

X Y

3 22

10 36

17 50

24 64

31 78

Finding the slope from word

problems

Slope from Word Problems

• The pitch of a roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8, what is the slope expressed as a positive number?

Slope from Word Problems

• A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five year period?

Drawing a line when given one point and the

slope

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

If you know the slope and one point on the line you can draw the line.

Example: slope is 1/3 and the point (-2,-1)

Now you draw a line.

• Given: slope is 2/3 and the point is (1,0)

• Given: slope is –3 and the point is (–2,4)

• Given: slope is 1 and the point is (2,3)

Finding a missing

coordinate.

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 y1)(x2 x1)

.

2 644 r

4 41 4 r

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

4 41 4 r

2 644 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)