m5 day review
Day 1 ‐ Direct and Inverse Variation
A. Recall
Direct Variation ‐ when the ratio between two quantities is a •
constant
It is described by an equation of the form y = kx, where k is a •
constant and y varies directly with respect to x.
Example: If a CD costs $12.00, then the relationship between the •
number of CD’s bought, x and the total cost, y is y = 12x
The graph of a direct variation is a line that passes through the origin
•
Inverse Variation ‐ is a function that is not linear
•
In an inverse variation, the relationship is xy = k. The product of two •
variables is a constant.
Another way to write the relationship is y = k/x
•
In both cases, k is the constant of variation and will be essential in •
solving direct and inverse variation problems.
Apr 25­5:03 PM
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B. Example 1. Write an equation of the direct variation that includes the given point
1. (‐4, ‐2)
2. (5, ‐3)
3. (‐1, 4)
Apr 28­9:57 AM
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C. Find the constant of variation if y varies inversely as x. Then write the inverse equation.
4. x = 12 and y = 3
5. x = 6 and y = ‐1/2 6. x = ‐2 and y = 3
Apr 28­9:58 AM
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D. Examples. Find the missing coordinate for the inverse variation.
7. The points (5, 6) and (3, y) are two points on the graph of an inverse variation. Find the missing y‐value.
8. The points (4, 8) and (x, 2) are two points on the graph of an inverse variation. Find the missing x‐value. Apr 28­9:58 AM
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May 2­7:52 AM
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E. Word problems. Use direct or inverse variation to solve the follow word problems. 9. A person’s paycheck p, varies directly with the number of hours worked t. For 16 hours of work, the paycheck is $124. What is the paycheck for someone who worked 24 hours?
10. The distance a spring will stretch varies directly with the amount of weight attached to the spring. If a spring stretches 9 inches with 100 lbs attached, how far with the spring stretch with 80 pounds attached?
Apr 28­9:59 AM
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11. The time t to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 55 mph?
12. The amount of days on a construction site varies inversely with the number of workers on the crew. If a 5 man crew takes 80 days to complete a job, how many days will the same job be completed with 20 workers?
Apr 28­9:59 AM
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May 2­8:18 AM
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