Lesson Worksheet: Linear Functions Mathematics • 8th Grade

In this worksheet, we will practice identifying, writing, and evaluating a linear function and completing its function table.


Fill in the input-output table for the function 𝑓(π‘₯)=5π‘₯+3.

Output …………
  • A3, 13, 23, 28
  • B3, 12, 23, 28
  • C0, 12, 23, 28
  • D3, 13, 23, 27
  • E0, 13, 23, 28


Evaluate 𝑓(2), given that 𝑓(π‘₯)=3π‘₯+7.

  • A𝑓(2)=3
  • B𝑓(2)=13
  • C𝑓(2)=12
  • D𝑓(2)=10
  • E𝑓(2)=7


Evaluate 𝑓(βˆ’π‘₯), given that 𝑓(π‘₯)=3π‘₯+7.

  • A𝑓(βˆ’π‘₯)=3βˆ’7π‘₯
  • B𝑓(βˆ’π‘₯)=βˆ’3π‘₯+7
  • C𝑓(βˆ’π‘₯)=3+7π‘₯
  • D𝑓(βˆ’π‘₯)=3π‘₯+7
  • E𝑓(βˆ’π‘₯)=3π‘₯βˆ’7


Given the function 𝑦=7+2π‘₯, what is the output of this function when the input is 4?


If π‘”βˆΆ{9,10,11,12,13}βŸΆβ„€οŠ°, where 𝑔(π‘₯)=17π‘₯βˆ’18 and 𝑔(π‘˜)=203, find the value of π‘˜.


Given that (π‘˜,2π‘˜) satisfies the relation π‘₯βˆ’2𝑦=βˆ’3, find the value of π‘˜.


Which of the following satisfies the relation π‘₯βˆ’π‘¦=βˆ’10?

  • A(βˆ’2,βˆ’2)
  • B(βˆ’16,6)
  • C(9,βˆ’1)
  • D(βˆ’12,βˆ’2)
  • E(βˆ’5,βˆ’15)


Given that (1,π‘Ž) satisfies the relation π‘¦βˆ’4π‘₯=7, find the value of π‘Ž.


Which of the following relations is satisfied by both the point (βˆ’1,1) and the point (0,3)?

  • A𝑓(π‘₯)=4π‘₯+3
  • B𝑓(π‘₯)=2π‘₯+3
  • C𝑓(π‘₯)=4π‘₯+5
  • D𝑓(π‘₯)=3π‘₯+4
  • E𝑓(π‘₯)=3π‘₯+3


Which of the following pairs all satisfy the relation π‘₯βˆ’π‘¦=βˆ’13?

  • A(βˆ’21,βˆ’8),(βˆ’19,βˆ’6),(βˆ’17,βˆ’4),(8,βˆ’5)
  • B(βˆ’8,βˆ’5),(βˆ’6,βˆ’7),(βˆ’4,βˆ’9),(8,βˆ’21)
  • C(βˆ’5,βˆ’8),(βˆ’7,βˆ’6),(βˆ’9,βˆ’4),(8,βˆ’21)
  • D(βˆ’5,βˆ’8),(βˆ’7,βˆ’6),(βˆ’9,βˆ’4),(βˆ’21,8)
  • E(βˆ’21,βˆ’8),(βˆ’19,βˆ’6),(βˆ’17,βˆ’4),(βˆ’5,8)


Given that (βˆ’7,βˆ’3) satisfies the relation 𝑓(π‘₯)=βˆ’3+3π‘₯𝑏, find the value of 𝑏.


Fill in the missing values given that the following pairs satisfy the relation 𝑦=3π‘₯βˆ’2: (8,), (11,), (13,), and (16,).

  • A26,35,41,50
  • B103,133,5,6
  • C24,33,39,48
  • D22,31,37,46
  • E2,3,113,143


Given that (0,2π‘š) satisfies the relation 𝑦=5π‘₯βˆ’8, find the value of π‘š.


Which of the following relations does the point (βˆ’5,2) not satisfy?

  • A𝑓(π‘₯)=βˆ’23βˆ’5π‘₯
  • B𝑓(π‘₯)=βˆ’5π‘₯2
  • C𝑓(π‘₯)=βˆ’19+5π‘₯3
  • D𝑓(π‘₯)=17+3π‘₯
  • E𝑓(π‘₯)=βˆ’18βˆ’4π‘₯


Which of the following does the point (βˆ’2,βˆ’2) satisfy?

  • A2π‘₯βˆ’π‘¦=2
  • Bπ‘₯+2𝑦=6
  • C2π‘₯βˆ’π‘¦=βˆ’2
  • Dπ‘₯+2𝑦=βˆ’2
  • E2π‘₯+𝑦=βˆ’2


Select the linear function whose graph is contained in the line 2π‘¦βˆ’3π‘₯+7=0.

  • AThe line with intercepts ο€Όβˆ’73,0 and ο€Ό0,βˆ’72
  • B𝑓(2)=βˆ’10, 𝑓(𝑛+1)=𝑓(𝑛)βˆ’32
  • C𝑓(π‘₯)=3π‘₯+72
  • D𝑓={(βˆ’3,βˆ’8),(βˆ’1,βˆ’5),(1,βˆ’2),(3,1)}


Find the coordinates of the points 𝑓(2), 𝑓(17), and 𝑓(31) given 𝑓(π‘₯)=π‘₯+12.

  • A(14,2),(43,17),(29,31)
  • B(14,2),(29,17),(43,31)
  • C(2,29),(17,14),(31,43)
  • D(2,14),(17,29),(31,43)


Evaluate 𝑓(4βˆ’π‘₯), given that 𝑓(π‘₯)=3π‘₯+7.

  • A𝑓(4βˆ’π‘₯)=βˆ’3π‘₯+19
  • B𝑓(4βˆ’π‘₯)=3π‘₯+12
  • C𝑓(4βˆ’π‘₯)=3π‘₯+18
  • D𝑓(4βˆ’π‘₯)=3π‘₯+7
  • E𝑓(4βˆ’π‘₯)=βˆ’3π‘₯+12


Consider a linear function 𝑓(π‘₯)=π‘šπ‘₯+𝑐.

Give an expression for 𝑓(π‘₯+Ξ”π‘₯)βˆ’π‘“(π‘₯).

  • Aπ‘š
  • Bπ‘šΞ”π‘₯+2𝑐
  • C𝑐
  • DΞ”π‘₯
  • Eπ‘šΞ”π‘₯

What can you conclude about the way a linear function grows?

  • AA linear function grows by a constant value (π‘šΞ”π‘₯+2𝑐) over a constant interval Ξ”π‘₯.
  • BA linear function grows by a constant value (Ξ”π‘₯) over a constant interval Ξ”π‘₯.
  • CA linear function grows by a constant value (π‘š) over a constant interval Ξ”π‘₯.
  • DA linear function grows by a constant value (π‘šΞ”π‘₯) over a constant interval Ξ”π‘₯.
  • EA linear function grows by a constant value (π‘šΞ”π‘₯+𝑐) over a constant interval Ξ”π‘₯.


Evaluate 𝑓(𝑇), given that 𝑓(π‘₯)=3π‘₯+7.

  • A𝑓(𝑇)=3𝑦+7
  • B𝑓(𝑇)=3π‘₯+7
  • C𝑓(𝑇)=3𝑇+7
  • D𝑓(𝑇)=3+7𝑇
  • E𝑓(𝑇)=𝑇+3


Answer the following questions for the functions 𝑦=3π‘₯βˆ’1 and 𝑦=βˆ’12π‘₯+52.

Complete the table of values for 𝑦=3π‘₯βˆ’1.

  • Aβˆ’7,βˆ’4,βˆ’1,2,5
  • Bβˆ’5,βˆ’2,βˆ’1,4,7
  • Cβˆ’6,βˆ’3,βˆ’1,3,6
  • Dβˆ’6,βˆ’3,3,3,6
  • Eβˆ’7,βˆ’4,3,2,5

Complete the table of values for 𝑦=βˆ’12π‘₯+52.

  • A1,12,52,βˆ’12,βˆ’1
  • B72,3,βˆ’12,2,32
  • C32,2,52,3,72
  • D1,12,βˆ’12,βˆ’12,βˆ’1
  • E72,3,52,2,32

Use the tables of values to determine the intersection point of the two graphs.

  • A(βˆ’1,βˆ’2)
  • B(2,1)
  • C(1,2)
  • D(βˆ’2,βˆ’1)
  • E(βˆ’2,0)


A bookstore sells used paperback books for $11.00 each and used hardcover books for $15.00 each. Find a function rule that shows the total selling price of both types of books, and then determine the price of 8 paperback and 3 hardcover books. Let 𝑑 represent the number of paperback books, 𝑣 the number of hardcover books, and 𝑑 the total selling price of both types of books.

  • A𝑑=11π‘‘βˆ’15𝑣, $43.00
  • B𝑑=11𝑑+15𝑣, $133.00
  • C𝑑=15𝑑+11𝑣, $153.00
  • D𝑑=8𝑑+3𝑣, $133.00
  • E𝑑=15π‘‘βˆ’11𝑣, $87.00


Find the range of 𝑓 given 𝑓(π‘₯)=βˆ’2π‘₯βˆ’3 where π‘₯∈{5,10}.

  • A{βˆ’23,βˆ’13}
  • B{βˆ’20,βˆ’10}
  • C{βˆ’20,2}
  • D{2,7}


Find 𝑑(1), 𝑑(4) and 𝑑(10) in coordinate form and the range of the function 𝑑(π‘₯)=3π‘₯+9.

  • A(1,βˆ’6),(4,3),(10,21), range ={βˆ’9,βˆ’6,βˆ’3,…}
  • B(βˆ’6,1),(3,4),(21,10), range ={βˆ’6,3,21}
  • C(1,12),(4,21),(10,39), range ={9,12,15,…}
  • D(12,1),(21,4),(39,10), range ={12,21,39}


Find 𝑏 given 𝑓(π‘₯)=5π‘₯+𝑏 where 𝑓(5)=17.

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