Lesson Worksheet: Direct Variation Mathematics • 7th Grade
In this worksheet, we will practice describing direct variation between two variables and using this to solve word problems.
Does vary directly with ? If so, what is the constant of variation?
- CYes, 1
True or False: A directly proportional relationship can always be represented by a straight line graph passing through the origin.
Chloe uses cups of flour to make 20 cookies. She makes a second batch using cups of flour to make 30 cookies. Is the amount of flour she uses directly proportional to the number of cookies she bakes?
Given that , and when , find the value of .
Given that varies directly with , and when , write an equation for in terms of .
A recipe for 4 people requires 440 g of spaghetti. The quantity of spaghetti is proportional to the number of people. What is the corresponding constant of proportionality (unit rate)?
- A110 g/person
- B440 g/person
- C1,760 persons/g
- D1,760 g/person
- E110 persons/g
The total cost for pizzas is proportional to the number of pizzas, as shown in the graph.
Find the unit rate.
- A$60 per pizza
- B30¢ per pizza
- C15¢ per pizza
- D$15 per pizza
- E$30 per pizza
The amount of caffeine in a cup of coffee is roughly 95 mg. What is the constant of proportionality, or unit rate, between the amount of caffeine ingested and the number of cups taken?
Points on a line are given in the table. Does vary directly with ? Is so, what is the constant of variation?
If , then .
The instructions on a packet of fertilizer state that 500 g will treat an area of 60 square meters if mixed correctly. How much fertilizer is needed to treat a garden whose area is 100 square meters? Give your answer to the nearest gram if necessary.
A website is selling e-books. It offers a discount of $0.50 for every referral you make. Is the amount of money saved by that offer directly proportional to the number of referrals you make?
Olivia was giving away coupons for a free appetizer at a local restaurant. She gave away 52 coupons an hour. Is the number of coupons she gave away proportional to the number of hours that she worked?