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Lesson: Solution of a Linear Equation by Graphing

In this lesson, we will learn how to find the solution of an equation that has only one root by graphing and verifying the answer algebraically.

Sample Question Videos

01:09

Worksheet • 7 Questions • 1 Video

Q1:

The graph in the diagram represents the function 𝑓 ( π‘₯ ) = 2 π‘₯ βˆ’ 7 . Without performing any calculation, use the graph to solve 2 π‘₯ βˆ’ 7 = 0 .

  • A π‘₯ = 3 . 5
  • B π‘₯ = βˆ’ 1 . 5
  • C π‘₯ = 3
  • D π‘₯ = 0
  • E π‘₯ = βˆ’ 7

Q2:

The graph in the diagram represents the function 𝑓 ( π‘₯ ) = βˆ’ 5 π‘₯ + 3 2 . Without performing any calculation, use the graph to solve βˆ’ 5 π‘₯ + 3 2 = 0 .

  • A π‘₯ = 0 . 3
  • B π‘₯ = 7 . 5
  • C π‘₯ = 3 . 3
  • D π‘₯ = βˆ’ 3 . 3
  • E π‘₯ = βˆ’ 0 . 3

Q3:

Consider the equation 𝑦 = βˆ’ 2 π‘₯ βˆ’ 4 . In the following, find a solution by filling the blank space.

( , 4 ) .

  • A ( βˆ’ 4 , 4 )
  • B ( 4 , 4 )
  • C ( 0 , 4 )
  • D ( βˆ’ 8 , 4 )
  • E ( 8 , 4 )

( , βˆ’ 8 ) .

  • A ( 2 , βˆ’ 8 )
  • B ( 4 , βˆ’ 8 )
  • C ( βˆ’ 2 , βˆ’ 8 )
  • D ( βˆ’ 6 , βˆ’ 8 )
  • E ( 6 , βˆ’ 8 )

( , βˆ’ 6 ) .

  • A ( 1 , βˆ’ 6 )
  • B ( βˆ’ 2 , βˆ’ 6 )
  • C ( βˆ’ 1 , βˆ’ 6 )
  • D ( βˆ’ 5 , βˆ’ 6 )
  • E ( 5 , βˆ’ 6 )

These solutions ( π‘₯ , 𝑦 ) can be plotted as seen in the figure. What will be true of any other solution plotted in the plane?

  • AThey will lie on the line.
  • BThey will lie on the π‘₯ -axis.
  • CThey will lie in the same quadrant.
  • DThey will not lie on the line.
  • EThey will not lie in the same quadrant.

Q4:

Which points in the graph represent a solution to the equation 𝑦 = 2 .

  • A 𝐸 , 𝐻
  • B 𝐸 , 𝐷 , 𝐻
  • C 𝐽 , 𝐹
  • D 𝐴 , 𝐡
  • E 𝐽

Q5:

Consider the equation 𝑦 = 2 π‘₯ + 3 . In the following, find a solution by filling the blank space.

( 3 , ) .

  • A ( 3 , 9 )
  • B ( 3 , 5 )
  • C ( 3 , 6 )
  • D ( 3 , 1 8 )
  • E ( 3 , 1 2 )

( βˆ’ 2 , ) .

  • A ( βˆ’ 2 , βˆ’ 1 )
  • B ( βˆ’ 2 , βˆ’ 4 )
  • C ( βˆ’ 2 , 1 )
  • D ( βˆ’ 2 , βˆ’ 2 )
  • E ( βˆ’ 2 , 2 )

( 1 , ) .

  • A ( 1 , 5 )
  • B ( 1 , 3 )
  • C ( 1 , 4 )
  • D ( 1 , 2 )
  • E ( 1 , 6 )

These solutions ( π‘₯ , 𝑦 ) can be plotted as seen in the figure. What will be true of any other solution plotted in the plane?

  • AThey will lie on the line.
  • BThey will lie on the π‘₯ -axis.
  • CThey will lie in the same quadrant.
  • DThey will not lie on the line.
  • EThey will not lie in the same quadrant.

Q6:

Which points in the graph represent a solution to the equation π‘₯ = 3 ?

  • A 𝐺 , 𝐼 , 𝐾
  • B 𝐡 , 𝐷
  • C 𝐴 , 𝐢 , 𝐸 , 𝐹
  • D 𝐺 , 𝐻 , 𝐼 , 𝐾
  • E 𝐽

Q7:

Which points in the graph represent a solution to the equation π‘₯ = βˆ’ 3 ?

  • A 𝐴 , 𝐢 , 𝐸 , 𝐹
  • B 𝐽
  • C 𝐺 , 𝐼 , 𝐾
  • D 𝐡 , 𝐷
  • E 𝐺 , 𝐻 , 𝐼 , 𝐾
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