slope
DESCRIPTION
Slope. run. rise. Slope =. Slope of a Linear Relationship. The Slope of a linear relationship is the steepness of the line. Slopes are seen everywhere. The steepness of the roof of a house is referred to as the pitch of the roof by home builders. - PowerPoint PPT PresentationTRANSCRIPT
Slope
Slope of a Linear Relationship
The Slope of a linear relationship is the steepness of the line.
rise
run
Slope =
riserun
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
112
112
1518
.
3 m
5 m
Determine the rate of change (pitch) of the roof.
35slope
2
3
3
3
32
slope
33
slope
1
Determine the rate of change of each staircase.
Determine the Slope.Which points will you use to determine rise and run?
= $5/hr
runrise
Slope
hr 420 $
20
4
Earnings
Number of Hours WorkedWhat 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)