Worksheet: Solution of a Linear Equation by Graphing

In this worksheet, we will practice finding the solution of an equation that has only one root by graphing and verifying the answer algebraically.

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

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

Q3:

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

( , 4 ) .

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

( , βˆ’ 8 ) .

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

( , βˆ’ 6 ) .

  • A ( βˆ’ 2 , βˆ’ 6 )
  • B ( βˆ’ 1 , βˆ’ 6 )
  • C ( 1 , βˆ’ 6 )
  • D ( 5 , βˆ’ 6 )
  • E ( βˆ’ 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 not lie on the line.
  • DThey will lie in the same quadrant.
  • EThey will not lie in the same quadrant.

Q4:

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

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

Q5:

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

( 3 , ) .

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

( βˆ’ 2 , ) .

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

( 1 , ) .

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

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 not lie on the line.
  • DThey will lie in the same quadrant.
  • EThey will not lie in the same quadrant.

Q6:

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

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

Q7:

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

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

Q8:

Let’s consider the equation 4 π‘₯ + 7 = 1 1 .

Karim says that to solve this equation graphically, one has to graph the function 𝑦 = 4 π‘₯ βˆ’ 4 . Nada says that she can solve it graphically without rearranging the equation in the form π‘Ž π‘₯ + 𝑏 = 0 but by graphing the function 𝑦 = 4 π‘₯ + 7 . Who is correct?

  • AOnly Nada
  • BOnly Karim
  • CNeither of them are correct.
  • DBoth of them are correct.

Without doing any calculation, solve the equation graphically.

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

Q9:

Which points in the graph represent a solution to the equation π‘₯ = 2 ?

  • A 𝐷
  • B 𝐴
  • C 𝐷 and 𝐹
  • D 𝐡 , 𝐢 , 𝐷 , and 𝐸
  • E 𝐡 , 𝐢 , and 𝐷

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