Lesson Worksheet: Linear Relationships Mathematics • 8th Grade

In this worksheet, we will practice identifying and graphing linear relationships.

Q1:

A school organized a trip where there is a fixed cost of 317pounds and the rest of the cost is dependent on the number of students attending. The total cost for a trip with 35 students is 597pounds. Find the total cost of the trip for 60 students given the relationship between the total cost and the number of students is linear.

Q2:

The graph shows the relationship between distance and time in a 160-metre race between a hare and a tortoise. Determine the winner, and then find the average speeds of the hare and the tortoise.

  • Athe hare, 179/mmin, 227/mmin
  • Bthe hare, 6/mmin, 227/mmin
  • Cthe tortoise, 179/mmin, 227/mmin
  • Dthe tortoise, 115/mmin, 227/mmin

Q3:

A boy was reading a book and found out that after reading for 2 hours he still had 344 pages left and after reading for 3 hours he had 43 pages left to read. Find the linear equation between the time 𝑑 and the number of pages left to read 𝑏.

  • A𝑏=βˆ’π‘‘βˆ’645
  • B𝑏=βˆ’301𝑑+946
  • C𝑏=301π‘‘βˆ’645
  • D𝑏=301𝑑+645

Q4:

Madison and Anthony are professional cyclists training for an upcoming race. The given graph represents the distance Madison traveled during one training session. The distance traveled by Anthony is given by the function 𝑑=18𝑑, where 𝑑 represents the distance in miles and 𝑑 represents the time in hours. Which of them is traveling faster?

  • AMadison
  • BAnthony

Q5:

Which of the following functions increases at a higher rate?

  • A(b)
  • B(a)

Q6:

The given figure shows the distance covered, 𝑑, in kilometres against the time of day, 𝑑, for two trains, A and B. Find the average speed of each train.

  • AAverage speed of train A =40/kmh, average speed of train B =45/kmh
  • BAverage speed of train A =45/kmh, average speed of train B =3334/kmh
  • CAverage speed of train A =60/kmh, average speed of train B =45/kmh
  • DAverage speed of train A =45/kmh, average speed of train B =45/kmh
  • EAverage speed of train A =54/kmh, average speed of train B =3334/kmh

Q7:

Which of the following is the same as the function 𝑔(π‘₯)=2π‘₯βˆ’3?

  • AThis is not a function.
  • B𝑧=2π‘§βˆ’3
  • Cπ‘₯=2π‘₯βˆ’3
  • D𝑦=2π‘₯βˆ’3
  • E𝑦=2π‘¦βˆ’3

Q8:

Daniel’s favorite drink is hot chocolate; he drinks it whenever it rains. As shown in the table, the number of cups of hot chocolate he drinks in a week is twice the number of rainy days that week. Which of the following statements is true?

Number of Rainy Days 1234
Number of Cups 2468
  • AThe dependent variable is the number of rainy days, and the independent variable is the number cups of hot chocolate that he drinks.
  • BThe dependent variable is the number of cups of hot chocolate that he drinks, and the independent variable is the number of rainy days.
  • CThe dependent variables are the number of cups of hot chocolate he drinks and the number of rainy days.
  • DThe independent variables are the number of cups of hot chocolate he drinks and the number of rainy days.

Q9:

Find the correct rule for the numbers in the table.

π‘₯24810
𝑦8163240
  • AMultiply π‘₯ by 4 to find 𝑦.
  • BAdd 2 to π‘₯ to find 𝑦.
  • CDivide π‘₯ by 4 to find 𝑦.
  • DDouble 𝑦 to find π‘₯.
  • ESubtract 2 from π‘₯ to find 𝑦.

Q10:

David is going to do a sponsored bike ride to raise money for charity. His uncle has promised to donate $12 more than the total amount that David raises. The graph and table show the relationship between the amount of money his uncle will donate (𝑑) and the amount of money that he raises (π‘š). Which of the following statements is true?

Amount raised (π‘š)12243648
Amount Donated (𝑑)24364860
  • AThe dependent variables are the amount of money that his uncle donates and the amount of money that David raises.
  • BThe independent variable is the amount of money that his uncle donates.
  • CThe independent variables are the amount of money that his uncle donates and the amount of money that David raises.
  • DThe dependent variable is the amount of money that David raises.
  • EThe dependent variable is the amount of money that his uncle donates.

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