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
![Page 1: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/1.jpg)
Slope
![Page 2: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/2.jpg)
Slope of a Linear Relationship
The Slope of a linear relationship is the steepness of the line.
rise
run
Slope =
riserun
![Page 3: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/3.jpg)
Slopes are seen everywhere.
![Page 4: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/4.jpg)
The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
![Page 5: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/5.jpg)
Give one reason why some homes have roofs which have a greater pitch.
There is less snow buildup in the wintertime.
![Page 6: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/6.jpg)
Engineers refer to the Slope of a road as the grade.
![Page 7: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/7.jpg)
They often represent the slope as a percentage.
![Page 8: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/8.jpg)
A grade of 8% would mean for every rise of 8 units there is a run of 100 units.
8100
= 8%
Slope = 8
100
![Page 9: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/9.jpg)
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
.
![Page 10: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/10.jpg)
3 m
5 m
Determine the rate of change (pitch) of the roof.
35slope
![Page 11: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/11.jpg)
2
3
3
3
32
slope
33
slope
1
Determine the rate of change of each staircase.
![Page 12: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/12.jpg)
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
![Page 13: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/13.jpg)
POSITIVE SLOPES
• Goes up to the right
![Page 14: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/14.jpg)
Negative Slope
• Goes down to the right
![Page 15: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/15.jpg)
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.
![Page 16: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/16.jpg)
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
![Page 17: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/17.jpg)
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?
![Page 18: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/18.jpg)
Try these
4
2
5
3
1
4321
4
2
5
3
1
4321
4
2
5
3
1
4321
![Page 19: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/19.jpg)
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
![Page 20: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/20.jpg)
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:•
![Page 21: Slope](https://reader036.vdocuments.site/reader036/viewer/2022062810/56815c2d550346895dca09b5/html5/thumbnails/21.jpg)
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)