Lesson Worksheet: Constant Rate of Change Mathematics

In this worksheet, we will practice finding the rate of change and using it to identify proportional and non-proportional linear relationships.


Which of the following interprets the rate of change of the data in the table?

Remaining Gas (gal)Miles Driven
  • AA decrease of 19 gallons per 50 miles
  • BA decrease of 19 gallons per 100 miles
  • CA decrease of 5 gallons per 100 miles
  • DA decrease of 5 gallons per 50 miles


Find the rate of change for the following graph.


A tank is being filled with water at a constant rate. The given graph shows the volume of water inside the tank with respect to time. What is the rate of change of the volume of the unfilled portion of the tank?


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


Nouf started doing exercise in order to lose weight. She lost 150 grams per week. Which of the following graphs represents Nouf’s situation?

  • A
  • B
  • C
  • D


Using the information in the given table, determine the rate of change in the number of seeds for every orange, and express your answer as a fraction.

Number of OrangesNumber of Seeds
  • A121
  • B365
  • C112
  • D118
  • E181


Two different tanks containing water were put outside to study the factors affecting the evaporation rate of water. The following figure shows the amount of water in each tank with respect to time.

Which tank has more water at the beginning?

  • ATank 1
  • BTank 2

In which tank is the evaporation rate higher?

  • ATank 2
  • BTank 1


A car manufacturer claims that the consumption of fuel of one of their cars is 5.2/100Lkm. Kayan measured the distance she covered with different volumes of fuel. She plotted her results and drew a line of best fit.

Did her car consume more or less fuel than what the car manufacturer had claimed?

  • ALess
  • BMore
  • CThe same


The graph below shows the relation between distance and time for a moving car. Is there a proportional relationship between the two quantities?

  • AYes
  • BNo


The graph represents the relationship between the perimeter and the diameter of a circle.

Find the constant of proportionality.

  • A2
  • B3
  • C𝜋2
  • D1
  • E𝜋

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