Lesson Worksheet: Solving Linear Equations Using Function Graphs Mathematics • 9th Grade

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(𝑥)=2𝑥7. Without performing any calculation, use the graph to solve 2𝑥7=0.

  • A𝑥=0
  • B𝑥=1.5
  • C𝑥=3.5
  • D𝑥=7
  • E𝑥=3

Q2:

The graph in the diagram represents the function 𝑓(𝑥)=5𝑥+32. Without performing any calculation, use the graph to solve 5𝑥+32=0.

  • A𝑥=3.3
  • B𝑥=7.5
  • C𝑥=0.3
  • D𝑥=3.3
  • E𝑥=0.3

Q3:

Consider the equation 𝑦=2𝑥4. In the following, find a solution by filling the blank space.

(,4).

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

(,8).

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

(,6).

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

These solutions (𝑥,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 𝑥-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 𝐵
  • B𝐽 and 𝐹
  • C𝐸, 𝐷, and 𝐻
  • D𝐽
  • E𝐸 and 𝐻

Q5:

Consider the equation 𝑦=2𝑥+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)

(2,).

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

(1,).

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

These solutions (𝑥,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 𝑥-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 𝑥=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 𝑥=3?

  • A𝐺,𝐻,𝐼,𝐾
  • B𝐵,𝐷
  • C𝐴,𝐶,𝐸,𝐹
  • D𝐽
  • E𝐺,𝐼,𝐾

Q8:

Which points in the graph represent a solution to the equation 𝑥=2?

  • A𝐴
  • B𝐷 and 𝐹
  • C𝐵,𝐶, and 𝐷
  • D𝐵,𝐶,𝐷, and 𝐸
  • E𝐷

Q9:

Let’s consider the equation 4𝑥+7=11.

David says that to solve this equation graphically, one has to graph the function 𝑦=4𝑥4. Isabella says that she can solve it graphically without rearranging the equation in the form 𝑎𝑥+𝑏=0 but by graphing the function 𝑦=4𝑥+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.

  • A𝑥=2
  • B𝑥=1
  • C𝑥=4
  • D𝑥=4
  • E𝑥=1

Q10:

Consider the function 𝑓(𝑥)=12𝑥+1. Use its given graph to solve the equation 12𝑥+1=0.

  • A𝑥=2
  • B𝑥=12
  • C𝑥=2
  • D𝑥=1
  • E𝑥=1

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