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Use a Graph to Solve an Equation

In this activity, students will learn how to use straight-line graphs to find solutions to linear equations.

'Use a Graph to Solve an Equation' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Solving Equations and Inequalities, Algebraic Equations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In other activities, we have covered solving linear equations using 'algebraic' methods. However, equations can also be solved using a graphical method which is what we consider in this activity.

On this graph we have two straight lines, y = 3x + 1 (in blue) and y = 4 (in red). We can see they meet (or intersect) at the point (1 , 4). This means that when x = 1 y = 4 and so x = 1 is a solution to the equation 3x + 1 = 4. 

We can add more horizontal lines to this graph and solve more related equations. 

The green line has equation y = -2 and so where it intersects the blue line we have the solution to 3x + 1 = -2. We see that the point of intersection is (-1 , -2) and so x = -1 is the solution to this equation.

Finally, the purple line has equation y = 8. Where it intersects the blue line we have the solution to the equation 3x + 1 = 8. You will notice this time that the x-value is not a whole number so we must estimate it. It is approximately x = 2.3 so that is our solution.

Note: we can check this last solution using the 'balancing' method. 

3x + 1 = 8

      -1    -1

3x      =  7

 ÷3      ÷3

             x    =   7/3 or 2.33333.....

 

Which of the equations below is represented by this graph?

3x + 3 = 6

3x + 6 = 3

3x - 3 = 6

3x - 6 = 3

Use the graph to find the solution to the equation 3x + 6 = 3. 

Choose from the options below.

x = 1

x = 3

x = -2

x = -1

Use this graph to match the four equations below to the four solutions.

Column A

Column B

2x - 1 = 4
x = 1.5
2x - 1 = 2
x = 2.5
2x - 1 = -3
x = -1
2x - 1 = -4
x = -1.5

Use the graph above to match the four equations below with the four solutions.

Column A

Column B

4x - 1 = 9
x = 1
4x - 1 = 3
x = -0.5
4x - 1 = -2
x = 2.5
4x - 1 = -5
x = -1

Use the graph above to solve the equation -3x + 4 = 1

Column A

Column B

4x - 1 = 9
x = 1
4x - 1 = 3
x = -0.5
4x - 1 = -2
x = 2.5
4x - 1 = -5
x = -1

The graph above can be used to solve the four equations below. Match each equation to its correct solution. 

Column A

Column B

2 - 2x = 6
x = 1.5
2 - 2x = 3
x = 2.5
2 - 2x = -1
x = -2
2 - 2x = -3
x = -0.5

Use the graph above to estimate the solutions to the three equations below. 

Column A

Column B

3x + 1 = 8
x = -1.3
3x = 1 = 3
x = 0.7
3x + 1 = -3
x = 2.3

Use the graph above to find the approximate solution to the equation 5x + 5 = 2.

Choose your solution from the options below.

x = -0.2

x = -0.6

x = -1.4

x = -1.8

Use the graph above to find an approximate solution to the equation 4 - 6x = -3. Give your answer to 1 decimal place.

x = -0.2

x = -0.6

x = -1.4

x = -1.8

Use the graph above to find an approximate solution to the equation 12 - 5x = 0. Give your answer correct to 1 decimal place.

x = -0.2

x = -0.6

x = -1.4

x = -1.8

  • Question 1

Which of the equations below is represented by this graph?

CORRECT ANSWER
3x + 6 = 3
EDDIE SAYS
The lines y = 3x + 6 and y = 3 interesect so the equation is 3x + 6 = 3.
  • Question 2

Use the graph to find the solution to the equation 3x + 6 = 3. 

Choose from the options below.

CORRECT ANSWER
x = -1
EDDIE SAYS
The point of intersection is (-1 , 3) so the solution is x = -1
  • Question 3

Use this graph to match the four equations below to the four solutions.

CORRECT ANSWER

Column A

Column B

2x - 1 = 4
x = 2.5
2x - 1 = 2
x = 1.5
2x - 1 = -3
x = -1
2x - 1 = -4
x = -1.5
EDDIE SAYS
y = 2x - 1 intersects y = 4 (blue) when x = 2.5. y = 2x - 1 intersects y = 2 (red) when x = 1.5. y = 2x - 1 intersects y = -3 (green) when x = -1. y = 2x - 1 intersects y = -4 (purple) when x = -1.5. Did you get them all correct?
  • Question 4

Use the graph above to match the four equations below with the four solutions.

CORRECT ANSWER

Column A

Column B

4x - 1 = 9
x = 2.5
4x - 1 = 3
x = 1
4x - 1 = -2
x = -0.5
4x - 1 = -5
x = -1
EDDIE SAYS
y = 4x -1 intersects y = 9 (blue) when x = 2.5 y = 4x -1 intersects y = 3 (red) when x = 1 y = 4x -1 intersects y = -2 (green) when x = -0.5 y = 4x -1 intersects y = -5 (purple) when x = -1
  • Question 5

Use the graph above to solve the equation -3x + 4 = 1

CORRECT ANSWER
EDDIE SAYS
The line y = -3x + 4 intersects the line y = 1 (green) when x = 1.
  • Question 6

The graph above can be used to solve the four equations below. Match each equation to its correct solution. 

CORRECT ANSWER

Column A

Column B

2 - 2x = 6
x = -2
2 - 2x = 3
x = -0.5
2 - 2x = -1
x = 1.5
2 - 2x = -3
x = 2.5
EDDIE SAYS
On the line y = 2 - 2x, when y = 6 x = -2 On the line y = 2 - 2x, when y = 3 x = -0.5 On the line y = 2 - 2x, when y = -1 x = 1.5 On the line y = 2 - 2x, when y = -3 x = 2.5
  • Question 7

Use the graph above to estimate the solutions to the three equations below. 

CORRECT ANSWER

Column A

Column B

3x + 1 = 8
x = 2.3
3x = 1 = 3
x = 0.7
3x + 1 = -3
x = -1.3
EDDIE SAYS
The line y = 3x + 1 interesects y = 8 (red) when x is approcimately 2.3 The line y = 3x + 1 interesects y = 3 (blue) when x is approcimately 0.7 The line y = 3x + 1 interesects y = -3 (green) when x is approcimately -1.3
  • Question 8

Use the graph above to find the approximate solution to the equation 5x + 5 = 2.

Choose your solution from the options below.

CORRECT ANSWER
x = -0.6
EDDIE SAYS
The line y = 5x + 5 intersects y = 2 (red) at approximately x = -0.6.
  • Question 9

Use the graph above to find an approximate solution to the equation 4 - 6x = -3. Give your answer to 1 decimal place.

CORRECT ANSWER
EDDIE SAYS
On the line y = 4 - 6x when y = -3 x is approximately 1.2.
  • Question 10

Use the graph above to find an approximate solution to the equation 12 - 5x = 0. Give your answer correct to 1 decimal place.

CORRECT ANSWER
EDDIE SAYS
The line y = 12 - 5x intersects the line y = 0 (the x-axis) at approximately x = 2.4.
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