4­2 Slope and Direct Variation.notebook
November 03, 2010
4­2 Slope and Direct Variation
It costs $2.25 per ringtone that you download for your cell phone. If you graph the ordered pairs, the slope of the line is 2.25.
Number of Ringtones
Total Cost ($)
x
y
0
0
1
2.25
2
4.50
3
6.75
4
9.00
The total cost y depends directly on the number of ringtones that you download x. The rate of change is constant.
Nov 13­10:39 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
Direct Variation:
Examples: Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points.
1.
2.
Nov 13­9:27 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
Example: Graph a Direct Variation
Graph each equation.
1. Graph y = x.
2. Graph y = 2x.
3.
Nov 13­11:12 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
Direct Variation Summary
­ Direct variation equations are of the
form y = kx, where k ≠ 0.
­ The graph of y = kx always passes through the origin.
­ The slope is positive if k > 0.
The slope is negative if k < 0.
* If you know that y varies directly as x, you can write a direct variation equation that relates the two quantities. Nov 13­11:18 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
Examples: Suppose y varies directly as x
and y = 28 and x = 7. a. Write a direct variation equation that relates x and y. b. Use the direct variation equation to find x when y = 52.
Nov 13­11:21 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
You try...
Suppose y varies directly as x, and y = 9 and x = ­3.
1. Write a direct variation equation that relates x and y. 2. Use the direct variation equation to find x when y = 15.
Nov 13­11:25 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
The migration of snow geese varies directly as the number of hours. A flock of snow geese migrated 375 miles in 7.5 hours.
a. Write a direct variation equation for the distance d flown in time t.
b. Estimate how many hours of flying time it would take the geese to migrate 3000 miles.
Nov 3­7:22 AM
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4­2 Slope and Direct Variation.notebook
November 03, 2010
Nov 3­8:47 AM
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