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1.04 Direct variation

Determine whether varies directly with . If so, find the constant of variation.


  1. Do x and y vary directly?

If so, find the constant of variation.


  1. Do x and y vary directly?

If so, find the constant of variation.


  1. Do x and y vary directly?

If so, find the constant of variation.

x / y
1 / -2
3 / -8
5 / 14

Do x and y vary directly?

If so, find the constant of variation.

  1. Determine whether varies directly with. If so, find the constant of variation and the direct variation equation.

x / y
5 / 20
15 / 60
45 / 180
135 / 540

Enter the letter of the correct answer:

  1. Yes; ;
  2. Yes; ;
  3. Yes; ;
  4. no

In problems 67 y varies directly with x. Find the direct variation equation. Then use the equation to solve the problem.

  1. If when , find when .
    Direct variation equation:
    Solution:
  1. If when , find when .
    Direct variation equation:
    Solution:

Solve each word problem.

  1. A salesperson’s commission varies directly with sales. For $1000 in sales, the commission is $85. What is the commission for $2300 in sales?
  1. For a given speed, the distance traveled varies directly with the time. Jan’s work is 6 miles away from her home and it takes her 12 minutes to reach the office. If Jake lives 4 miles from the office and travels at the same speed as Jan, how long will it take him to reach the office?
  1. The number of desks a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 147 desks in 30 hours. How many hours will it take to produce 250 desks? (Round answer to the nearest hour if necessary.)