Worksheet: Proportional Equations

In this worksheet, we will practice writing an equation to describe the proportional relationship of data in a table or a graph.

Q1:

For the following table, find the algebraic equation that shows the proportional relationship between 𝑥 and 𝑦.

𝑥 6 7 8
𝑦 12 14 16
  • A 𝑦 = 2 𝑥
  • B 𝑥 = 6 𝑦
  • C 𝑥 = 2 𝑦
  • D 𝑥 = 𝑦
  • E 𝑦 = 6 𝑥

Q2:

Which of the below represents the percentage of 74 commuters from 430 commuters?

  • A 𝑛 = 7 4 × 4 . 3
  • B 𝑛 = 7 4 × 4 3 0
  • C 4 3 0 7 4 = 𝑛 1 0 0
  • D 7 4 4 3 0 = 𝑛 1 0 0
  • E 𝑛 = 0 . 7 4 × 4 3 0

Q3:

Determine the four proportional numbers of which the fourth proportional equals the square of the second, the first is less than the second by 1, and the third is 72.

  • A 1 0 , 9 , 7 2 , 8 1 or 7,8,72,64
  • B 8 , 9 , 7 2 , 1 8 or 9,8,72,16
  • C 8 , 9 , 7 2 , 8 1 or 9,8,72,64
  • D 1 0 , 9 , 7 2 , 1 8 or 7,8,72,16

Q4:

For every three dishes Isabella cleans, Emma cleans five. This represents a proportional relationship. Which of the following equations can be used to determine how many dishes Emma cleans if Isabella cleans 38?

  • A 𝑥 3 = 3 8 5
  • B 𝑥 5 = 3 3 8
  • C 3 5 = 3 8 𝑥
  • D 3 5 = 𝑥 3 8

Q5:

Jennifer plotted the distance, in miles, she cycled against the time, in hours, on her last ride and drew a line of best fit. Her friend Benjamin says that to estimate the distance in miles he covers in a given number of hours, he uses the equation 𝑑=15𝑡.

Who is the faster cyclist?

  • AJennifer
  • BBenjamin

Q6:

It takes Teresa 8 minutes to fill her 60-liter bathtub from a single faucet. Which of the following lines represents the volume of water she gets from her faucet against the time during which the faucet is open?

  • Athe orange one
  • Bthe black one
  • Cthe blue one
  • Dthe green one

Q7:

How many graphs represent a proportional relationship between 𝑦 and 𝑥?

Q8:

The graph shows the amount of saturated fat contained in a given mass of butter.

A 100 g portion of olive oil contains 14 g of saturated fat. Which contains a larger proportion of saturated fat, butter or olive oil?

  • Aolive oil
  • Bbutter

Q9:

Michael sold 3 dozen eggs for $5.28. Which of the following points in the graph represents the rate at which Michael sold the eggs?

  • Apoint 𝐵
  • Bpoint 𝐶
  • Cpoint 𝐴

Q10:

The given table shows the total distance traveled by a bus driving at a constant speed. Using this information, determine how far the bus will have traveled after 10 hours.

Time (h) 2 5.7 6 7
Distance (mi) 142 404.7 426 497

Q11:

Emma walks to school every day. Find her speed from the distance-time graph.

Q12:

Given that the relation between the velocity 𝑣 m/s and the time 𝑡 seconds is 𝑣=9.8𝑡, what is the value of 𝑣 when 𝑡=8?

Q13:

Based on the given graph, which statement could be true?

  • AA merchant will earn $100 if he sells $1,000 worth of merchandise.
  • BA merchant will earn $3,200 if he sells $3,200 worth of merchandise.
  • CA merchant will earn $750 if he sells $15,000 worth of merchandise.
  • DA merchant will earn money if he has no sales.

Q14:

Amelia has 212 cups of raisins, which is only enough to make 78 of her usual trail mix. How many more cups of raisins does she need to finish making her trail mix?

  • A 5 1 4 c
  • B 2 6 7 c
  • C 1 5 5 5 6 c
  • D 1 5 8 c
  • E 5 5 1 4 c

Q15:

Select the graph that shows a proportional relationship.

  • A
  • B
  • C
  • D
  • E

Q16:

Which of the following proportions can be used to find the score, as a percentage, on a quiz that had 25 questions?

  • A 1 8 1 0 0 = 2 5 𝑥
  • B 1 8 2 5 = 𝑥 1 0 0
  • C 1 8 1 0 0 = 𝑥 2 5
  • D 𝑥 1 8 = 2 5 1 0 0
  • E 2 5 1 8 = 𝑥 1 0 0

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