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Worksheet: Direct Variation

Q1:

The velocity, 𝑣 , of an object in m/s is directly proportional to the time, 𝑑 , in seconds. This relationship can be expressed in the equation 𝑣 = 9 . 8 𝑑 . Find the value of 𝑑 when 𝑣 = 6 3 7 m/s.

Q2:

Given that 𝑦 varies directly as π‘₯ , write an equation for 𝑦 in terms of π‘₯ using π‘˜ as a non-zero constant.

  • A 𝑦 = π‘˜ π‘₯ 2
  • B 𝑦 = π‘˜ π‘₯
  • C 𝑦 = π‘˜ π‘₯ 2
  • D 𝑦 = π‘˜ π‘₯

Q3:

If 𝑦 ∝ π‘₯ and π‘₯ = 7 5 when 𝑦 = 2 5 , find the value of 𝑦 when π‘₯ = 3 0 .

Q4:

A gas station charges $3 per gallon for gasoline, and $6 for a car wash. Daniel never washes his car there because he thinks it is too expensive, but he often buys gasoline there. Is the total money he spends at the station directly proportional to the amount of gasoline he buys?

  • Ayes
  • Bno

Q5:

Does 𝑦 vary directly with π‘₯ ? If so, what is the constant of variation?

π‘₯ 2 4 6 8
𝑦 3 4 5 6
  • A yes, 1 1 2
  • B yes, 3 4
  • C yes, 1
  • Dno
  • E yes, 5 6

Q6:

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)?

Q7:

The total cost for pizzas is proportional to the number of pizzas, as shown in the graph.

Find the unit rate.

  • A15Β’ per pizza
  • B$30 per pizza
  • C30Β’ per pizza
  • D$15 per pizza
  • E$60 per pizza

Q8:

The amount of meat required to feed a captive lion is given by the equation 𝑀 = 9 𝑑 , where 𝑀 is the weight of the meat in kilograms needed to feed a lion for 𝑑 days. What is the unit rate of this proportional relationship?

Q9:

Points on a line are given in the table. Does 𝑦 vary directly with π‘₯ ? Is so, what is the constant of variation?

π‘₯ 3 6 9 12
𝑦 2 4 6 8
  • A no
  • B yes, 1 1 2
  • C yes, 2 3

Q10:

A body’s weight on Earth is 120 kg and its weight on The Moon is 20 kg. Given that both weights are directly proportional to each other, find the body’s weight on The Moon when its weight on Earth is 126 kg.

Q11:

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?

  • Ayes
  • Bno

Q12:

Given that 𝑦 varies directly with π‘₯ , and 𝑦 = 1 8 when π‘₯ = 6 , write an equation for 𝑦 in terms of π‘₯ .

  • A 𝑦 = 6 π‘₯
  • B 𝑦 = π‘₯ 3
  • C 𝑦 = π‘₯ 6
  • D 𝑦 = 3 π‘₯
  • E 𝑦 = π‘₯ + 1 2

Q13:

To attend a festival, Daniel needs a separate ticket for each day. He was given free tickets to attend the first three days, then paid $30 per ticket for each of the other days he attended. Was the amount of money he spent on tickets directly proportional to the number of tickets he had?

  • Ano
  • Byes

Q14:

Victoria 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?

  • A yes
  • B no

Q15:

Determine whether the following statement is true or false: A directly proportional relationship can always be represented by a straight line graph passing through the origin.

  • Atrue
  • Bfalse

Q16:

Given that π‘₯ ∝ 𝑦 , which of the following is equal to 𝑦 𝑦 1 2 ?

  • A π‘₯ π‘₯ 2 1 2 2
  • B π‘₯ π‘₯ 2 1
  • C π‘₯ π‘₯ 1 2 2
  • D π‘₯ π‘₯ 1 2

Q17:

Olivia uses 2 1 2 cups of flour to make 20 cookies. She makes a second batch using 3 3 4 cups of flour to make 30 cookies. Is the amount of flour she uses directly proportional to the number of cookies she bakes?

  • Ayes
  • Bno

Q18:

Given that 𝑦 varies directly as π‘₯ 2 , write an equation for 𝑦 in terms of π‘₯ using π‘˜ as a non-zero constant.

  • A 𝑦 = π‘˜ π‘₯
  • B 𝑦 = π‘˜ π‘₯
  • C 𝑦 = π‘˜ π‘₯ 2
  • D 𝑦 = π‘˜ π‘₯ 2

Q19:

Which of the given graphs represents the direct variation between π‘₯ and 𝑦 ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

Q20:

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?