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.

• The table describes a linear function. Find the slope, m, from 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?
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  16
• Since this is a linear equation that includes the point (0, 0), this is a direct variation with m = k. Write the equation for the variation.

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  What value should you substitute for k in the equation y = kx?
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  y = 16x
• Find the number of gallons of milk needed to serve 240 students.

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  Does the value of 240 correspond with x or y?
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  15 gallons
  
  y = 16x
  
  240 over 16 240 16 = 16x over 16 16x 16
  
  15 = x

Practice

1. Jose earns $9 per hour. Below is a chart showing the relationship between the number of hours Jose works and the amount he earns.
   
   

   Jose's Earnings
   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?
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   $432
2. Dawson Elementary School is having a book sale. For each book sold, the school earns $2.30. Below is a chart showing the relationship between the number of books Dawson Elementary School sold and the amount of money raised in the book sale.
   
   

   Dawson Elementary School Book Sale
   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?
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   56 books