Worksheet: Solving Linear Equations Using Function Graphs

In this worksheet, we will practice solving linear equations using function graphs and verifying the answer algebraically.

Q1:

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

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

Q2:

The graph in the diagram represents the function 𝑓(π‘₯)=βˆ’5π‘₯+32. Without performing any calculation, use the graph to solve βˆ’5π‘₯+32=0.

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

Q3:

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

( , 4 ) .

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

( , βˆ’ 8 ) .

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

( , βˆ’ 6 ) .

  • A ( βˆ’ 1 , βˆ’ 6 )
  • B ( βˆ’ 5 , βˆ’ 6 )
  • C ( βˆ’ 2 , βˆ’ 6 )
  • D ( 1 , 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 π‘₯-axis.
  • BThey will lie on the line.
  • CThey will not lie in the same quadrant.
  • DThey will lie in the same quadrant.
  • EThey will not lie on the line.

Q4:

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

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

Q5:

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

( 3 , ) .

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

( βˆ’ 2 , ) .

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

( 1 , ) .

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

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 in the same quadrant.
  • BThey will lie on the π‘₯-axis.
  • CThey will lie on the line.
  • 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 𝐡 , 𝐷
  • B 𝐴 , 𝐢 , 𝐸 , 𝐹
  • C 𝐺 , 𝐼 , 𝐾
  • D 𝐺 , 𝐻 , 𝐼 , 𝐾
  • E 𝐽

Q7:

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

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

Q8:

Let’s consider the equation 4π‘₯+7=11.

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

  • ANeither of them are correct.
  • BBoth of them are correct.
  • COnly David
  • DOnly Isabella

Without doing any calculation, solve the equation graphically.

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

Q9:

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

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

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