Slopes (or steepness ) of lines are seen everywhere.

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Slopes (or steepness ) of lines are seen everywhere. The steepness of the roof of a house is referred to as the pitch of the roof by home builders. Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.

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Presentation Transcript

Give one reason why some homes have roofs which have a greater pitch.

There is less snow build up in the wintertime.

Slopes and Lines

rise

run

The slope of a line is the steepnessof the line.

8

100

A grade of 8% would mean for every run of 100 units, there is a rise of 8 units.

= 8%

The steepness of wheelchair ramps is of great importance to handicapped persons.

1

12

The slope of wheelchair ramps is usually about

If the rise is 1.5 m, what is the run?

Ans: 18 m

Determine the slope of the line.

5 cm

9 cm

We use the letter m because in French the word for “to go up” is monter.

Because the slope is a ratio, there are no units such as cm or cm2.

9

3

Determine the slope.

12

10

8

6

4

2

0

2

4

8

6

10

14

12

– 5

7

Determine the slope.

12

10

8

6

4

2

12

0

4

8

6

10

14

2

7

Determine the slope.

12

10

8

6

4

2

Horizontal lines have a slope of zero.

0

2

4

8

6

10

14

12

6

Determine the slope.

12

10

8

6

4

Vertical lines have no slope.

2

0

2

4

8

6

10

14

12

negative

positive

undefined

zero

Summary: Types of Slopes

Determine the slope of this line.

Which points will you use to determine rise and run?

40

5

= 8

Draw a line which has a slope of

Draw a line which has a slope of 2

Draw a line which has a slope of…

b) 3

a) – 3

1

–3

3

1

1

–3

3

1

9

3

Remember this example?

12

10

8

6

4

2

0

2

4

8

6

10

14

12

Formula for Slope

When given the coordinates of two points on

the line: and

the slope is the difference of the y-coordinates divided by the difference of the x-coordinates.

To represent the difference, we use the Greek letter for d, delta, in the formula.

Slope = =

Summary

Slope = = =

Examples:

Find the slope of the line passing through the two points. Use your answer to decide whether the line is increasing, decreasing, vertical, or horizontal.

a) and

b) and

c) and

a) decreasing

b) vertical

c) horizontal