Slope

Slope of a Linear Relationship

The Slope of a linear relationship is the steepness of the line.

rise

run

Slope =

rise

run

Slopes 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 buildup in the wintertime.

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

They often represent the slope as a percentage.

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

8100

= 8%

Slope = 8

100

The steepness of wheelchair ramps is of great importance for safety.

Slope of wheelchair ramp =

112

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

Answer: 18 m because

1

1 2

1

12

15

18

.

3 m

5 m

Determine the rate of change (pitch) of the roof.

3

5slope

2

3

3

3

3

2slope

3

3slope

1

Determine the rate of change of each staircase.

Determine the Slope.Which points will you use to determine rise and run?

= $5/hr

run

riseSlope

hr 4

20 $20

4

Earnings

Number of Hours Worked

What does this rate of change represent?

The hourly wage

POSITIVE SLOPES

• Goes up to the right

Negative Slope

• Goes down to the right

STEEPNESS OF SLOPE

• The greater the _ Constant of variation_(steapness)__, the ___Greater__ the slope!

• (i.e. a slope of -10 is __Greater_______ than a slope of 8)

• A ski hill has two runs with a slope of 6% and 10%. Represent their slopes in a graph.

HOW DO WE MEASURE SLOPE?

• Slope compares the __Rise__ to the run__ to determine the __Slope______ steepness

• Slope can be represented by the letter __m___

• The formula for slope is given by:

• Slope = Rise/Run

Try it

• A ski jump is 90 metres high and takes up a horizontal distance of 32 metres along the ground. What is the slope of the jump?

Try these

4

2

5

3

1

4321

4

2

5

3

1

4321

4

2

5

3

1

4321

Answers

• Slope =-5/2 2/3 3/1 =3

4

2

5

3

1

4321

4

2

5

3

1

4321

4

2

5

3

1

4321

Lets apply this stuff

• A line segment has an endpoint at (5, 4) and a slope of -2/3. Find another point on the line.

• Using a graph:– therefore (8,2)

• Using the coordinates:•

Using coordinates

• A line segment has an endpoint at (5, 4) and a slope of -2/3. Find another point on the line.

• 5+3=8

• 4-2 = 2 therefore (8,2)