Worksheet: Linear Relationships

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.

  • A 𝑏 = 3 0 1 𝑑 + 6 4 5
  • B 𝑏 = 3 0 1 𝑑 βˆ’ 6 4 5
  • C 𝑏 = βˆ’ 3 0 1 𝑑 + 9 4 6
  • D 𝑏 = βˆ’ 𝑑 βˆ’ 6 4 5

Q4:

Chloe and Noah are professional cyclists training for an upcoming race. The given graph represents the distance Chloe traveled during one training session. The distance traveled by Noah 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?

  • AChloe
  • BNoah

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 kilometers 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.
  • B 𝑧 = 2 𝑧 βˆ’ 3
  • C π‘₯ = 2 π‘₯ βˆ’ 3
  • D 𝑦 = 2 π‘₯ βˆ’ 3
  • E 𝑦 = 2 𝑦 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 1 2 3 4
Number of Cups 2 4 6 8
  • 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:

If 𝑓(π‘₯) is a linear function, find an equation for it given 𝑓(4)=βˆ’1 and 𝑓(9)=2.

  • A 𝑓 ( π‘₯ ) = βˆ’ 1 7 5 βˆ’ 3 5 π‘₯
  • B 𝑓 ( π‘₯ ) = βˆ’ 1 7 5 + 3 5 π‘₯
  • C 𝑓 ( π‘₯ ) = βˆ’ 1 7 5 π‘₯ + 3 5
  • D 𝑓 ( π‘₯ ) = βˆ’ 1 7 5 + 5 3 π‘₯

Q10:

Find the correct rule for the numbers in the table.

π‘₯ 2 4 8 10
𝑦 8 16 32 40
  • 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.

Q11:

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) 12 24 36 48
Amount Donated (𝑑) 24 36 48 60
  • 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.

Q12:

A school organized a trip where there is a fixed cost of 409pounds and the rest of the cost is dependent on the number of students attending. The total cost for a trip with 18 students is 463pounds. Find the total cost of the trip for 49 students given the relationship between the total cost and the number of students is linear.

Q13:

The given figure shows the distance covered, 𝑑, in kilometers 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 =60/kmh
  • BAverage speed of train A =60/kmh, average speed of train B =2623/kmh
  • CAverage speed of train A =60/kmh, average speed of train B =60/kmh
  • DAverage speed of train A =80/kmh, average speed of train B =2623/kmh

Q14:

A boy was reading a book and found out that after reading for 7 hours he still had 256 pages left and after reading for 8 hours he had 57 pages left to read. Find the linear equation between the time 𝑑 and the number of pages left to read 𝑏.

  • A 𝑏 = 1 9 9 𝑑 + 4 5 5
  • B 𝑏 = 1 9 9 𝑑 βˆ’ 4 5 5
  • C 𝑏 = βˆ’ 𝑑 βˆ’ 4 5 5
  • D 𝑏 = βˆ’ 1 9 9 𝑑 + 1 , 6 4 9

Q15:

William went to the market. He bought 3 kilograms of apples for $9 and 2 kilograms of oranges for $8.

If William represents the prices of apples and oranges against the quantity (in kilograms), what type of graph does he get?

  • AA graph with two curved lines
  • BA graph with two straight lines which both pass through the origin
  • CAn S curve
  • DA parabola
  • EA graph with two straight lines which do not pass through the origin

In his graph, which fruit does the top line represent?

  • AOranges
  • BThere is no top line because the lines are coincident.
  • CApples

Q16:

The following graph shows the money that Scarlett earns.

Write an equation to represent the relationship between dollars and time.

  • A 𝑑 = 1 6 0 𝑑
  • B 𝑑 = 6 0 𝑑
  • C 𝑑 = 1 4 0 𝑑
  • D 𝑑 = 4 0 𝑑
  • E 𝑑 = 8 0 𝑑

Q17:

What function is represented in the figure below?

  • A 𝑓 ( π‘₯ ) = βˆ’ π‘₯ + 1
  • B 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 1
  • C 𝑓 ( π‘₯ ) = 2 π‘₯
  • D 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯

Q18:

Does the shown figure represent a linear function?

  • Ayes
  • Bno

Q19:

Complete the following statement: The graph of a function is .

  • Aa set of circles
  • Ba set of lines
  • Ca set of ordered pairs consisting of an input and the corresponding output

Q20:

Benjamin read 2 books of 150 pages each in 3 months. At his school, the teacher showed a graph of the number of pages that pupils in his year group are expected to read against time.

Does Benjamin read less or more than what is expected from his school?

  • Athe same
  • Bmore
  • Cless

What is Benjamin’s reading rate?

  • A300 pages per month
  • B100 pages per month
  • C80 pages per month
  • D150 pages per month
  • E50 pages per month

What is the expected rate?

  • A300 pages per month
  • B50 pages per month
  • C100 pages per month
  • D80 pages per month
  • E150 pages per month

Q21:

After graphing the function using the given table of values, determine whether it could be a linear function.

π‘₯ -value βˆ’ 1 0 4
𝑦 -value 5 4 0
  • AIt is a nonlinear function.
  • BIt could be a linear function.

Q22:

Determine whether the given table of values must be from a nonlinear function, or could be from a linear function.

π‘₯ -value 0 2 4 6
𝑦 -value 3 4 5 6
  • AIt could be from a linear function.
  • BIt must be from a nonlinear function.

Q23:

A car manufacturer claims that the consumption of fuel of one of their cars is 5.2/100Lkm. Jennifer 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

Q24:

Which line graphs the function 𝑦=2π‘₯+3?

  • A 𝐴
  • B 𝐢
  • C 𝐡
  • D 𝐷

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