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.

  • Aπ‘₯=0
  • Bπ‘₯=βˆ’1.5
  • Cπ‘₯=3.5
  • Dπ‘₯=βˆ’7
  • Eπ‘₯=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.

  • Aπ‘₯=3.3
  • Bπ‘₯=7.5
  • Cπ‘₯=0.3
  • Dπ‘₯=βˆ’3.3
  • Eπ‘₯=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?

  • A𝐴 and 𝐡
  • B𝐽 and 𝐹
  • C𝐸, 𝐷, and 𝐻
  • D𝐽
  • E𝐸 and 𝐻

Q5:

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

(3,).

  • A(3,5)
  • B(3,18)
  • C(3,9)
  • D(3,12)
  • 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?

  • AB, D
  • BA, C, E, F
  • CG, I, K
  • DG, H, I, K
  • EJ

Q7:

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

  • A𝐺,𝐻,𝐼,𝐾
  • B𝐡,𝐷
  • C𝐴,𝐢,𝐸,𝐹
  • D𝐽
  • E𝐺,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.

  • Aπ‘₯=2
  • Bπ‘₯=βˆ’1
  • Cπ‘₯=βˆ’4
  • Dπ‘₯=4
  • Eπ‘₯=1

Q9:

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

  • A𝐴
  • B𝐷 and 𝐹
  • C𝐡,𝐢, and 𝐷
  • D𝐡,𝐢,𝐷, and 𝐸
  • E𝐷

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