Worksheet: Graphing Linear Functions

In this worksheet, we will practice graphing linear functions.

Q1:

Let us consider the function 𝑓(𝑥)=8𝑥11.

Fill in the table.

𝑥 −1 0 1
𝑦 = 𝑓 ( 𝑥 )
  • A
    𝑥 −1 0 1
    𝑦 = 𝑓 ( 𝑥 ) −19 −11 −3
  • B
    𝑥 −1 0 1
    𝑦 = 𝑓 ( 𝑥 ) −3 −11 3
  • C
    𝑥 −1 0 1
    𝑦 = 𝑓 ( 𝑥 ) −19 8 3
  • D
    𝑥 −1 0 1
    𝑦 = 𝑓 ( 𝑥 ) 3 −11 −3
  • E
    𝑥 −1 0 1
    𝑦 = 𝑓 ( 𝑥 ) 3 0 −3

Identify the three points that lie on the line 𝑦=8𝑥11.

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

Q2:

Consider the function 𝑓(𝑥)=2𝑥+5.

Fill in the table.

𝑥 −2 0 2
𝑦 = 𝑓 ( 𝑥 )
  • A
    𝑥 −2 0 2
    𝑦 = 𝑓 ( 𝑥 ) 1 5 1
  • B
    𝑥 −2 0 2
    𝑦 = 𝑓 ( 𝑥 ) 8 −2 1
  • C
    𝑥 −2 0 2
    𝑦 = 𝑓 ( 𝑥 ) 9 5 1
  • D
    𝑥 −2 0 2
    𝑦 = 𝑓 ( 𝑥 ) 5 0 −1
  • E
    𝑥 −2 0 2
    𝑦 = 𝑓 ( 𝑥 ) 1 −2 9

Identify the three points that lie on the line 𝑦=2𝑥+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=𝑥+7?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following graphs represents the equation 2𝑥3𝑦=18?

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

Consider the equation 3𝑦=6𝑥+32.

Rearrange the equation into the form 𝑦=𝑚𝑥+𝑐.

  • A 𝑦 = 𝑥 1 2
  • B 𝑦 = 2 𝑥 1
  • C 𝑦 = 2 𝑥 + 1
  • D 𝑦 = 𝑥 + 1 2
  • E 𝑦 = 2 𝑥 1 2

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

  • ASlope = 2, 𝑦-intercept = 12
  • BSlope = 2, 𝑦-intercept = 1
  • CSlope = 1, 𝑦-intercept = 12
  • DSlope = 2, 𝑦-intercept = 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=15𝑥 shows how time 𝑥 relates to the distance 𝑦. Which graph represents this function?

  • A
  • B
  • C
  • D
  • E

Q8:

Consider the linear equation 𝑦=2𝑥+3.

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

  • A ( 0 , 3 ) and 23,0
  • B ( 3 , 0 ) and 0,32
  • C ( 0 , 3 ) and 32,0
  • D ( 0 , 3 ) and 32,0
  • E ( 3 , 0 ) and 0,32

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

  • AA
  • BE
  • CD
  • DC
  • EB

Q9:

Consider the linear equation 2𝑦3𝑥+5=0.

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

  • A 5 2 , 0 and 53,0
  • B 0 , 2 5 and 35,0
  • C 0 , 2 5 and 35,0
  • D 0 , 5 2 and 53,0
  • E 0 , 5 2 and 53,0

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