SLOPE Monday 11/14 Effects of SLOPE with changes to m and b.
Rate of Change and Slope Monday, November 1, 2010.
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Transcript of Rate of Change and Slope Monday, November 1, 2010.
![Page 1: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/1.jpg)
Rate of Changeand
Slope
Monday, November 1, 2010
![Page 2: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/2.jpg)
Definition
• Rate of change allows you to see the relationship between two quantities that are changing.
![Page 3: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/3.jpg)
Formula
Rate of change =
![Page 4: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/4.jpg)
Finding the Rate of Change Using a Table
Cost of Renting a Computer
Number of Days
Rental Charge
1 $60
2 $75
3 $90
4 $105
5 $120
Rate of change =
The rate of change is $15 per day after the first day of rental.
![Page 5: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/5.jpg)
Finding Rate of Change Using a Graph
• Rate of change =
• Use two points
• Divide
• Simplify
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Slope Formula
• Slope = =
where x2 – x1 0
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Find Slope Using Two Points
• Slope =
• Find the slope of the line through A(-2, 1) and B (5, 7).
• the slope of Line AB is
![Page 8: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/8.jpg)
Find the slope of the line through each pair of points.
• C (2, 5) and D (4, 7)– Slope is 1.
• P (-1, 4) and Q (3, -2)– Slope is
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Horizontal and Vertical Lines
• Slope =
• Substitute two points
• The slope of a horizontal line is 0.
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• Slope =
• Substitute two points
• The slope of the vertical line is undefined.
![Page 11: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/11.jpg)
Find the slope of the line.
Slope = 0
![Page 12: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/12.jpg)
Find the slope of the line.
Slope = undefined
![Page 13: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/13.jpg)
Find the slope of the line.
Slope = undefined
![Page 14: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/14.jpg)
Find the slope of the line.
Slope = 0
![Page 15: Rate of Change and Slope Monday, November 1, 2010.](https://reader038.fdocuments.us/reader038/viewer/2022110400/56649da05503460f94a8c4e9/html5/thumbnails/15.jpg)
Closure
• What are two ways to find the slope of a line?– You can count the units of rise and run between
two points on graph. Or you can find the difference of the y-coordinates, and, in the same order, the difference of the x-coordinates. Then write the quotient of the difference of the y-coordinates divided by the difference of the x-coordinates.