In the previous sections, the direct variation problems were solved through the relationship to a linear function. Tables are also used when solving or graphing linear functions; therefore, they can be used to solve direct variation problems, too.
Example: The school cafeteria had to purchase gallons of milk to feed the students. Each student is served 1 cup of milk. Below is a chart showing the number of cups in a gallon. Find the number of gallons of milk needed to serve 240 students.
Drag the correct number of cups in the given gallon of milk.
First, find the function rule of the table.
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What is the ratio of the change in the cups of milk to the change in the gallons of milk? Interactive popup. Assistance may be required. 16Interactive popup. Assistance may be required.
What value should you substitute for k in the equation y = kx? Interactive popup. Assistance may be required. y = 16xInteractive popup. Assistance may be required.
Does the value of 240 correspond with x or y? Interactive popup. Assistance may be required. 15 gallonsJose's Earnings |
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Number of Hours Worked | 1 |
2 |
3 |
4 |
Amount of Money Earned | 9 |
18 |
27 |
36 |
The amount of money Jose earns varies directly as the number of hours that he works. One week, Jose worked 48 hours. Find the amount he earned.
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What is the constant of variation in this situation? Interactive popup. Assistance may be required. $432Dawson Elementary School Book Sale |
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Number of Books Sold | 1 |
2 |
3 |
4 |
Amount of Money Raised | $2.30 |
$4.60 |
$6.90 |
$9.20 |
If the school earns $128.80, find the number of books sold.
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Does the $128.80 correspond with the number of books sold, or the amount of money raised? Interactive popup. Assistance may be required. 56 books