AI generatedAlgebraKS3 / GCSE

Solving an equation by adding a line to a graph

Solving an equation by adding a line to a graph.

  • State the equation before solving it.
  • Follow the operation labels between lines. Apply the same operation to both sides.
  • Substitute the answer into the original equation to check that both sides agree.

Example 1

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.

Example 2

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.

Your turn

Question 1

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Check answer
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.
Question 2

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Check answer
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.
Question 3

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Check answer
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.
Question 4

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Check answer
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.
Question 5

Use the graph to solve the equation.

Read both intersection x-coordinates; substitute to check.
Read both intersection x-coordinates; substitute to check.
Check answer
Draw the left-hand and right-hand expressions as two separate graphs.Read the -coordinate of each intersection. The two graph heights are equal there. Check by substituting into the original equation.