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.

  • A 𝑦 = 3 π‘₯ + 8
  • B 𝑦 = 3 π‘₯ + 1 8
  • C 𝑦 = 8 π‘₯ + 3
  • D 𝑦 = π‘₯ 3 + 8
  • E 𝑦 = 3 π‘₯ βˆ’ 8

Q2:

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

  • A π‘š = 1 0 and 𝑐=30
  • B π‘š = 2 and 𝑐=6
  • C π‘š = 3 0 and 𝑐=10
  • D π‘š = 1 2 and 𝑐=16
  • E π‘š = 6 and 𝑐=2

Q3:

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

π‘₯ -value βˆ’ 2 βˆ’ 1 0
𝑦 -value 3 4 5
  • A 𝑦 = βˆ’ π‘₯ + 5
  • B 𝑦 = π‘₯ βˆ’ 5
  • C 𝑦 = 5 π‘₯ + 1
  • D 𝑦 = π‘₯ + 5
  • E 𝑦 = 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.

  • A π‘š = 1 , 𝑏 = βˆ’ 1
  • B π‘š = 1 3 , 𝑏 = βˆ’ 3
  • C π‘š = 1 , 𝑏 = 1
  • D π‘š = βˆ’ 1 3 , 𝑏 = 3
  • E π‘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§.

  • A 𝑦 βˆ’ 1 π‘š π‘₯  
  • B 𝑦 + π‘š π‘₯  
  • C 𝑦 βˆ’ π‘š π‘₯  
  • D βˆ’ 𝑦 βˆ’ π‘š π‘₯  
  • E π‘š 𝑦 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‘₯.

  • A 𝑦 βˆ’ π‘₯ 𝑦 βˆ’ π‘₯    
  • B π‘₯ βˆ’ π‘₯ 𝑦 βˆ’ 𝑦    
  • C 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯    
  • D 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯    
  • E 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯    

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

  • A 𝑦 βˆ’ 𝑦 = π‘š π‘₯ 
  • B 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ ) 
  • C 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ )  
  • D 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ )  
  • E 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ )  

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

  • A 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ π‘₯     
  • B 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ )      
  • C 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ )     
  • D 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ )      
  • E 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 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?

  • A 𝑏 represents the slope of the graph of the function, and π‘š represents the π‘₯-intercept of the graph of the function.
  • B π‘š represents the slope of the graph of the function, and 𝑏 represents the π‘₯-intercept of the graph of the function.
  • C π‘š represents the slope of the graph of the function, and 𝑏 represents the 𝑦-intercept of the graph of the function.
  • D 𝑏 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?

  • A 𝑓 ( π‘₯ ) = 2 π‘₯ + 6
  • B 𝑓 ( π‘₯ ) = 2 π‘₯ βˆ’ 6 
  • C 𝑓 ( π‘₯ ) = 2 π‘₯ βˆ’ 6
  • D 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯ βˆ’ 6
  • E 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯ + 6

Q15:

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

  • A βˆ’ 5 π‘₯ = 2
  • B 2 𝑦 = π‘₯ + 5
  • C βˆ’ 5 𝑦 = 2
  • D 2 𝑦 = βˆ’ 5
  • E 2 π‘₯ = 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.

  • A 3 π‘₯ + 2 𝑦 = 1
  • B π‘₯ βˆ’ 𝑦 = βˆ’ 1
  • C π‘₯ + 2 𝑦 = 1
  • D π‘₯ βˆ’ 2 𝑦 = 1
  • E 3 π‘₯ βˆ’ 2 𝑦 = 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.

  • A 2 π‘₯ βˆ’ 𝑦 + 1 6 = 0
  • B π‘₯ + 2 𝑦 + 1 6 = 0
  • C βˆ’ π‘₯ + 2 𝑦 + 1 6 = 0
  • D βˆ’ π‘₯ + 2 𝑦 βˆ’ 1 6 = 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.

  • A βˆ’ 6 π‘₯ + 7 𝑦 βˆ’ 3 8 = 0
  • B 6 π‘₯ + 7 𝑦 βˆ’ 3 8 = 0
  • C 7 π‘₯ + 6 𝑦 + 1 0 = 0
  • D 6 π‘₯ + 7 𝑦 + 1 0 = 0

Q19:

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

  • A 4 π‘₯ + 3 𝑦 = 3 6
  • B 3 π‘₯ βˆ’ 4 𝑦 = βˆ’ 3 6
  • C 4 π‘₯ βˆ’ 3 𝑦 = 3 6
  • D 3 π‘₯ + 4 𝑦 = βˆ’ 3 6
  • E 3 π‘₯ βˆ’ 4 𝑦 = 3 6

Q20:

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

  • A 2 π‘₯ βˆ’ 5 𝑦 = 2 0
  • B 5 π‘₯ + 2 𝑦 = βˆ’ 2 0
  • C 5 π‘₯ + 2 𝑦 = 2 0
  • D 5 π‘₯ βˆ’ 2 𝑦 = 2 0
  • E 2 π‘₯ + 5 𝑦 = 2 0

Q21:

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

  • A 3 π‘₯ + 2 𝑦 + 1 5 = 0
  • B 3 π‘₯ + 2 𝑦 βˆ’ 1 5 = 0
  • C 3 π‘₯ βˆ’ 7 𝑦 βˆ’ 1 5 = 0
  • D 2 π‘₯ + 3 𝑦 βˆ’ 1 5 = 0

Q22:

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

  • A 4 π‘₯ + 3 𝑦 = βˆ’ 5
  • B βˆ’ 4 π‘₯ + 3 𝑦 = 5
  • C 𝑦 = 5 3 + 4 3 π‘₯
  • D 𝑦 = 5 3 βˆ’ 4 3 π‘₯
  • E 4 π‘₯ + 3 𝑦 = 5

Q23:

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

  • A 3 π‘₯ + 1 2 𝑦 = 4
  • B 3 π‘₯ βˆ’ 1 2 𝑦 = 4
  • C 3 π‘₯ + 1 2 𝑦 = 4
  • D βˆ’ 3 π‘₯ + 1 2 𝑦 = 4 8
  • E βˆ’ 3 π‘₯ + 1 2 𝑦 = 4

Q24:

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

  • A βˆ’ π‘₯ + 3 𝑦 = 7
  • B βˆ’ π‘₯ + 3 𝑦 = 2 1
  • C π‘₯ + 3 𝑦 = 7
  • D π‘₯ + 3 𝑦 = 2 1
  • E π‘₯ βˆ’ 3 𝑦 = 2 1

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
  • B βˆ’ 1 . 5 , decreasing
  • C3, decreasing
  • D2, decreasing

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