Worksheet: Graphing Linear Functions

In this worksheet, we will practice graphing linear functions.

Q1:

Let us consider the function 𝑓(π‘₯)=8π‘₯βˆ’11.

Fill in the table.

π‘₯βˆ’101
𝑦=𝑓(π‘₯)
  • A
    π‘₯βˆ’101
    𝑦=𝑓(π‘₯)βˆ’19βˆ’11βˆ’3
  • B
    π‘₯βˆ’101
    𝑦=𝑓(π‘₯)βˆ’3βˆ’113
  • C
    π‘₯βˆ’101
    𝑦=𝑓(π‘₯)βˆ’1983
  • D
    π‘₯βˆ’101
    𝑦=𝑓(π‘₯)3βˆ’11βˆ’3
  • E
    π‘₯βˆ’101
    𝑦=𝑓(π‘₯)30βˆ’3

Identify the three points that lie on the line 𝑦=8π‘₯βˆ’11.

  • AA, C, E
  • BI, H, G
  • CA, C, D
  • DH, I, G
  • EB, C, D

Q2:

Consider the function 𝑓(π‘₯)=βˆ’2π‘₯+5.

Fill in the table.

π‘₯βˆ’202
𝑦=𝑓(π‘₯)
  • A
    π‘₯βˆ’202
    𝑦=𝑓(π‘₯)151
  • B
    π‘₯βˆ’202
    𝑦=𝑓(π‘₯)8βˆ’21
  • C
    π‘₯βˆ’202
    𝑦=𝑓(π‘₯)951
  • D
    π‘₯βˆ’202
    𝑦=𝑓(π‘₯)50βˆ’1
  • E
    π‘₯βˆ’202
    𝑦=𝑓(π‘₯)1βˆ’29

Identify the three points that lie on the line 𝑦=βˆ’2π‘₯+5.

  • AH, F, J
  • BA, C, E
  • CH, I, G
  • DB, C, D
  • EI, H, J

Q3:

Which of the following graphs represents the equation 𝑦=βˆ’π‘₯+7?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following graphs represents the equation 2π‘₯βˆ’3𝑦=18?

  • A
  • B
  • C
  • D
  • E

Q5:

Matthew rides his bike at a steady rate of 15 miles per hour. The function 𝑦=15π‘₯ shows how time π‘₯ relates to the distance 𝑦. Which graph represents this function?

  • A
  • B
  • C
  • D
  • E

Q6:

Consider the equation 3𝑦=6π‘₯+32.

Rearrange the equation into the form 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=π‘₯βˆ’12
  • B𝑦=2π‘₯βˆ’1
  • C𝑦=2π‘₯+1
  • D𝑦=π‘₯+12
  • E𝑦=2π‘₯βˆ’12

What are the slope and 𝑦-intercept of the equation?

  • ASlope = 2, 𝑦-intercept = βˆ’12
  • BSlope = 2, 𝑦-intercept = 1
  • CSlope = 1, 𝑦-intercept = βˆ’12
  • DSlope = 2, 𝑦-intercept = βˆ’1
  • ESlope =1, 𝑦-intercept = 12

Use the slope and intercept to identify the correct graph of the equation.

  • A
  • B
  • C
  • D
  • E

Q7:

Noah rides his bike at a steady rate of 15 miles per hour. The function 𝑦=15π‘₯ shows how time π‘₯ relates to the distance 𝑦. Which graph represents this function?

  • A
  • B
  • C
  • D
  • E

Q8:

Consider the linear equation 𝑦=2π‘₯+3.

By finding the π‘₯- and 𝑦- intercepts, state the coordinates (0,𝑦)-intercept and (π‘₯,0)-intercept where the graph of the function crosses the axes.

  • A(0,3) and ο€Όβˆ’23,0
  • B(βˆ’3,0) and ο€Ό0,32
  • C(0,3) and ο€Όβˆ’32,0
  • D(0,βˆ’3) and ο€Ό32,0
  • E(3,0) and ο€Ό0,βˆ’32

Hence, identify which of these is the line of the equation.

  • AA
  • BE
  • CD
  • DC
  • EB

Q9:

Consider the linear equation 2π‘¦βˆ’3π‘₯+5=0.

By finding the π‘₯- and 𝑦-intercepts, state the coordinates (0,𝑦)-intercept and (π‘₯,0)-intercept where the graph of the function crosses the axes.

  • Aο€Όβˆ’52,0 and ο€Ό53,0
  • Bο€Ό0,25 and ο€Όβˆ’35,0
  • Cο€Ό0,βˆ’25 and ο€Ό35,0
  • Dο€Ό0,βˆ’52 and ο€Ό53,0
  • Eο€Ό0,52 and ο€Όβˆ’53,0

Hence, identify which of these is the line of the equation.

  • AD
  • BE
  • CB
  • DA
  • EC

Q10:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑦=βˆ’3π‘₯+1
  • B𝑦=3π‘₯βˆ’1
  • C𝑦=3π‘₯+1
  • D𝑦=βˆ’3π‘₯βˆ’1
  • E𝑦=13π‘₯βˆ’1

Q11:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑦=4π‘₯
  • B𝑦=4π‘₯+1
  • C𝑦=4π‘₯βˆ’1
  • D𝑦=βˆ’4π‘₯+1
  • E𝑦=βˆ’4π‘₯

Q12:

Jacob wants to draw the graph of the linear equation 𝑦=3π‘₯βˆ’4.

He plotted the points with π‘₯-coordinates 0, 1, 2, 3, and 4 but made one mistake.

Which point is incorrect?

  • AE
  • BB
  • CD
  • DA
  • EC

What are the correct coordinates of this point?

  • A(4,5)
  • B(4,4)
  • C(3,6)
  • D(3,4)
  • E(3,5)

Q13:

Consider the linear equation 𝑦=5βˆ’2π‘₯.

We can draw a straight line to represent this equation. Complete the table to find the coordinates of points on the line.

π‘₯βˆ’2βˆ’1012
𝑦
  • A9, 7, 6, 3, 1
  • B9, 7, 5, 3, 1
  • C1, 3, 5, 7, 9
  • D9, 7, 5, 3, 2

Which of the following is the graph of the equation?

  • A
  • B
  • C
  • D

Which of these points is not on the line?

  • A(4,βˆ’3)
  • B(βˆ’3,11)
  • C(βˆ’4,13)
  • D(3,βˆ’1)
  • E(6,βˆ’6)

Q14:

By making a table of values, determine which of the following graphs represents the equation 𝑦=12π‘₯+1.

  • A
  • B
  • C
  • D
  • E

Q15:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑦=5π‘₯+1
  • B𝑦=βˆ’15π‘₯βˆ’1
  • C𝑦=βˆ’15π‘₯+1
  • D𝑦=15π‘₯βˆ’1
  • E𝑦=15π‘₯+1

Q16:

Which of the following is the function represented by the shown graph?

  • Aπ‘₯=23𝑦+2
  • B𝑦=23π‘₯+2
  • C𝑦=2π‘₯+23
  • D𝑦=32π‘₯+2
  • E𝑦=23π‘₯βˆ’2

Q17:

Which of the following graphs represents the equation 𝑦=4βˆ’3π‘₯?

  • A
  • B
  • C
  • D
  • E

Q18:

By making a table of values, determine which of the following is the function represented by the graph shown.

  • A𝑦=βˆ’13π‘₯βˆ’4
  • B𝑦=13π‘₯+4
  • C𝑦=13π‘₯βˆ’4
  • D𝑦=βˆ’13π‘₯+4
  • E𝑦=βˆ’3π‘₯+4

Q19:

Which of the following graphs represents the equation 𝑦=2π‘₯+3?

  • A
  • B
  • C
  • D
  • E

Q20:

By graphing the functions 𝑓(π‘₯)=3π‘₯βˆ’2 and 𝑔(π‘₯)=4βˆ’π‘₯, state the point at which they intersect.

  • A(1.5,2.5)
  • B(1.7,2.1)
  • C(0.5,3.5)
  • D(3,7)

Q21:

The given figure shows the graphs of the functions 𝑓(π‘₯)=3π‘₯+11 and 𝑔(π‘₯)=βˆ’12π‘₯+12. What is the point where 𝑓(π‘₯)=𝑔(π‘₯)?

  • A(2,βˆ’3)
  • B(1,βˆ’3)
  • C(βˆ’3,1)
  • D(βˆ’4.2,2.6)
  • E(βˆ’3,2)

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