Worksheet: Linear Functions in Different Forms

In this worksheet, we will practice writing linear functions in different forms, such as standard form and slope–intercept form.

Q1:

Write a linear function in the form 𝑦=π‘šπ‘₯+𝑏, that has a slope of 3 and a 𝑦-intercept of 8.

  • A𝑦=3π‘₯+8
  • B𝑦=3π‘₯+18
  • C𝑦=8π‘₯+3
  • D𝑦=π‘₯3+8
  • E𝑦=3π‘₯βˆ’8

Q2:

Calculate the slope π‘š and the 𝑦-intercept 𝑐 for the function 5𝑦=10π‘₯+30.

  • Aπ‘š=10 and 𝑐=30
  • Bπ‘š=2 and 𝑐=6
  • Cπ‘š=30 and 𝑐=10
  • Dπ‘š=12 and 𝑐=16
  • Eπ‘š=6 and 𝑐=2

Q3:

Write the equation that represents the linear function shown in the given table.

π‘₯-valueβˆ’2βˆ’10
𝑦-value345
  • A𝑦=βˆ’π‘₯+5
  • B𝑦=π‘₯βˆ’5
  • C𝑦=5π‘₯+1
  • D𝑦=π‘₯+5
  • E𝑦=π‘₯5+1

Q4:

What is the 𝑦-intercept of the line passing through (βˆ’2,βˆ’16) and (1,βˆ’4)?

Q5:

True or false: The equation of a line intercepting the vertical axis at 𝑏 is 𝑦=π‘šπ‘₯+𝑏.

  • Afalse
  • Btrue

Q6:

True or false: The equation of a line passing through the origin is 𝑦=π‘šπ‘₯.

  • Atrue
  • Bfalse

Q7:

Which of the following graphs represents the equation 𝑦=4π‘₯βˆ’1?

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

What is the relation between the point (0,4) and the line 𝑦=2π‘₯βˆ’8?

  • AIt lies on the line.
  • BIt is the 𝑦-intercept of the line.
  • CIt is below the line.
  • DIt is the π‘₯-intercept of the line.
  • EIt lies above the line.

Q10:

Find the slope π‘š and the 𝑦-intercept 𝑏 of this straight line.

  • Aπ‘š=1, 𝑏=βˆ’1
  • Bπ‘š=13, 𝑏=βˆ’3
  • Cπ‘š=1, 𝑏=1
  • Dπ‘š=βˆ’13, 𝑏=3
  • Eπ‘š=βˆ’1, 𝑏=1

Q11:

A straight line is defined by the equation 𝑦=π‘šπ‘₯+𝑐.

Given that the point (π‘₯,𝑦) lies on the line, find an expression for 𝑐 in terms of π‘š, π‘₯, and π‘¦οŠ§.

  • Aπ‘¦βˆ’1π‘šπ‘₯
  • B𝑦+π‘šπ‘₯
  • Cπ‘¦βˆ’π‘šπ‘₯
  • Dβˆ’π‘¦βˆ’π‘šπ‘₯
  • Eπ‘šπ‘¦βˆ’π‘₯

Given also that the point (π‘₯,𝑦) lies on the line and π‘š is the slope of the line, find an expression for π‘š in terms of π‘¦οŠ§, π‘¦οŠ¨, π‘₯, and π‘₯.

  • Aπ‘¦βˆ’π‘₯π‘¦βˆ’π‘₯
  • Bπ‘₯βˆ’π‘₯π‘¦βˆ’π‘¦οŠ¨οŠ§οŠ¨οŠ§
  • Cπ‘¦βˆ’π‘¦π‘₯βˆ’π‘₯
  • Dπ‘¦βˆ’π‘¦π‘₯βˆ’π‘₯
  • Eπ‘¦βˆ’π‘¦π‘₯βˆ’π‘₯

By substituting in for 𝑐 and factorizing out π‘š, find the formula for the equation of the line.

  • Aπ‘¦βˆ’π‘¦=π‘šπ‘₯
  • B𝑦=π‘š(π‘₯βˆ’π‘₯)
  • Cπ‘¦βˆ’π‘¦=π‘š(π‘₯βˆ’π‘₯)
  • Dπ‘¦βˆ’π‘¦=π‘š(π‘₯βˆ’π‘₯)
  • Eπ‘¦βˆ’π‘¦=π‘š(π‘₯βˆ’π‘₯)

Substitute in your expression for π‘š to complete your formula.

  • Aπ‘¦βˆ’π‘¦=π‘¦βˆ’π‘¦π‘₯βˆ’π‘₯π‘₯
  • Bπ‘¦βˆ’π‘¦=π‘¦βˆ’π‘¦π‘₯βˆ’π‘₯(π‘₯βˆ’π‘₯)
  • C𝑦=π‘¦βˆ’π‘¦π‘₯βˆ’π‘₯(π‘₯βˆ’π‘₯)
  • Dπ‘¦βˆ’π‘¦=π‘¦βˆ’π‘¦π‘₯βˆ’π‘₯(π‘₯βˆ’π‘₯)
  • Eπ‘¦βˆ’π‘¦=π‘¦βˆ’π‘¦π‘₯βˆ’π‘₯(π‘₯βˆ’π‘₯)

Q12:

The general form for the equation of any linear function is 𝑦=π‘šπ‘₯+𝑏. What do π‘š and 𝑏 represent?

  • A𝑏 represents the slope of the graph of the function, and π‘š represents the π‘₯-intercept of the graph of the function.
  • Bπ‘š represents the slope of the graph of the function, and 𝑏 represents the π‘₯-intercept of the graph of the function.
  • Cπ‘š represents the slope of the graph of the function, and 𝑏 represents the 𝑦-intercept of the graph of the function.
  • D𝑏 represents the slope of the graph of the function, and π‘š represents the 𝑦-intercept of the graph of the function.

Q13:

What is the 𝑦-intercept of the function 𝑦=5π‘₯+7?

Q14:

Which of the following equations represents the function drawn on the graph?

  • A𝑓(π‘₯)=2π‘₯+6
  • B𝑓(π‘₯)=2π‘₯βˆ’6
  • C𝑓(π‘₯)=2π‘₯βˆ’6
  • D𝑓(π‘₯)=βˆ’2π‘₯βˆ’6
  • E𝑓(π‘₯)=βˆ’2π‘₯+6

Q15:

Determine the equation of the straight line given in the diagram.

  • Aβˆ’5π‘₯=2
  • B2𝑦=π‘₯+5
  • Cβˆ’5𝑦=2
  • D2𝑦=βˆ’5
  • E2π‘₯=βˆ’5

Q16:

Find the equation of the straight line that passes through the points (1,1) and (3,4). Give your answer in standard form.

  • A3π‘₯+2𝑦=1
  • Bπ‘₯βˆ’π‘¦=βˆ’1
  • Cπ‘₯+2𝑦=1
  • Dπ‘₯βˆ’2𝑦=1
  • E3π‘₯βˆ’2𝑦=1

Q17:

Given 𝐴(0,βˆ’8), 𝐡(βˆ’5,βˆ’8), and 𝐢(9,βˆ’6), find the general equation of the straight line that passes through point 𝐴 and bisects 𝐡𝐢.

  • A2π‘₯βˆ’π‘¦+16=0
  • Bπ‘₯+2𝑦+16=0
  • Cβˆ’π‘₯+2𝑦+16=0
  • Dβˆ’π‘₯+2π‘¦βˆ’16=0

Q18:

Find the Cartesian equation of the straight line passing through the point (βˆ’4,2) and parallel to the straight line whose equation is 6π‘₯+7𝑦+3=0.

  • Aβˆ’6π‘₯+7π‘¦βˆ’38=0
  • B6π‘₯+7π‘¦βˆ’38=0
  • C7π‘₯+6𝑦+10=0
  • D6π‘₯+7𝑦+10=0

Q19:

Write the equation represented by the graph shown. Give your answer in the form π‘Žπ‘₯+𝑏𝑦=𝑐.

  • A4π‘₯+3𝑦=36
  • B3π‘₯βˆ’4𝑦=βˆ’36
  • C4π‘₯βˆ’3𝑦=36
  • D3π‘₯+4𝑦=βˆ’36
  • E3π‘₯βˆ’4𝑦=36

Q20:

Write the equation represented by the graph shown. Give your answer in the form π‘Žπ‘₯+𝑏𝑦=𝑐.

  • A2π‘₯βˆ’5𝑦=20
  • B5π‘₯+2𝑦=βˆ’20
  • C5π‘₯+2𝑦=20
  • D5π‘₯βˆ’2𝑦=20
  • E2π‘₯+5𝑦=20

Q21:

A line has slope βˆ’32 and passes through the point (5,0). What is the equation of this line?

  • A3π‘₯+2𝑦+15=0
  • B3π‘₯+2π‘¦βˆ’15=0
  • C3π‘₯βˆ’7π‘¦βˆ’15=0
  • D2π‘₯+3π‘¦βˆ’15=0

Q22:

Write the linear equation 3𝑦=5βˆ’4π‘₯ in standard form.

  • A4π‘₯+3𝑦=βˆ’5
  • Bβˆ’4π‘₯+3𝑦=5
  • C𝑦=53+43π‘₯
  • D𝑦=53βˆ’43π‘₯
  • E4π‘₯+3𝑦=5

Q23:

Write the linear equation 𝑦=3π‘₯+412 in standard form.

  • A3π‘₯+12𝑦=4
  • B3π‘₯βˆ’12𝑦=4
  • C3π‘₯+12𝑦=4
  • Dβˆ’3π‘₯+12𝑦=48
  • Eβˆ’3π‘₯+12𝑦=4

Q24:

Write the linear equation 𝑦=13π‘₯+7 in standard form.

  • Aβˆ’π‘₯+3𝑦=7
  • Bβˆ’π‘₯+3𝑦=21
  • Cπ‘₯+3𝑦=7
  • Dπ‘₯+3𝑦=21
  • Eπ‘₯βˆ’3𝑦=21

Q25:

Given that a linear function contains the points (2,3) and (0,6), find the slope of the function and state whether it is increasing or decreasing.

  • A1.5, increasing
  • Bβˆ’1.5, decreasing
  • C3, decreasing
  • D2, decreasing

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.