Slope

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.

Engineers refer to the slope of a road as the grade.

They often refer to the slope as a percentage.

Slopes and Lines

rise

run

The slope of a line is the steepness of the line.

riseslope =

run

8 ft

100 ft

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

8slope =

100

= 8%

The steepness of wheelchair ramps is of great importance to those who use them.

The slope of wheelchair ramps is usuallyabout 1 foot rise for every 12 feet of run.

1 ft12 ft

If the rise is 2 feet, what is the run?

Answer: 24 feet

3 m

5 m

Determine the slope (pitch) of the roof.

5

3m m

m

2

3m

3

3m

Determine the slope of the staircase.

23

33= 1

6 yd

3 secrise

runm

2

4 6 1080 12 14

4

6

8

10

12

2

Determine the slope.D

ista

nce

(ya

rds)

Time (seconds)

m = 6 yards 3 secondsm = 2 yds/sec

– 5

75

7m

rise

runm

Determine the slope.

2

4 6 1080 12 14

4

6

8

10

12

2

7

0

7m

rise

runm

0m

Horizontal lines have a slope of zero.2

4 6 1080 12 14

4

6

8

10

12

2

Determine the slope.

6 6

0m

rise

runm

(undefined)

Vertical lines have slopes which are undefined.

2

4 6 1080 12 14

4

6

8

10

12

2

Determine the slope.

cannot divide by zero!

rise

runm

positive

negative

zeroundefined

Summary: Types of Slopes

Slope MountainSki Resort

Positive slope, + work

Negative slope, - work

Zero slope is zero fun! Undefined

slope.

Oh No!!!!

T. Merrill 2005

Slope of line through 2 points

• To find the slope of a line through 2 given points we use the formula

• For example, Find the slope of a line that goes through (-3, 5) and (2, 18)

12

12

xx

yyslope

x1 y1 x2 y2

12

12

xx

yyslope

185 2-3

5

13

Determine the slope of this line.

5

40

riseslope =

run

40

5m = 8

How can you find slope when counting lines is just too much?

Let’s take a closer look . . .

(7, 70)

(2, 30)

Δx

Δy

In general,

(x2, y2)

(x1, y1)

Δx

Δy

Determine the slope of the line segment.

(20, 7)

(80, 5)x1 y1

x2 y2

Draw a line which has a slope of 1

2

Draw a line which has a slope of 2

Draw a line which has a slope of 5

6

–5

6

–5

6

What Type of Slope is Shown?

Positive Slope

Negative Slope

Zero Slope

No Slope/Undefined

Slope of a Table• In a table we can use the same formula. Pick any

two pairs in the table for coordinates

x y

-4 -17

1 -2

3 4

8 19

10 25

Pick any two rows. If it is linear it will be the same

no matter which two rows you pick

12

12

xx

yyslope

x1

x2

y1

y2 13

24

slope13

24

2

6 3

Conclusion

• Slope is:

• Describe the slope of each of the following

the rate of change of a line

run

riseslope

12

12

xx

yyslope

Negative slope Undefined/ No slope

Positive slope Zero/0 slope