Parallel lines and a misleading claim

Choose your method, connect the parts and explain your conclusions. These original questions include written reasoning and sketches as well as exact answer checks.

Suggested marks guide how much working to show. The site does not automatically award examination marks for proofs, diagrams or methods. Use scaffolded fluency practice when you need a hint first.

Level 2 / FSMQ. Course filters use selected objective mappings; none of these tasks establishes complete paper coverage.

Before you start

Straight lines and gradients. Read the relevant method, then decide which parts you can solve without hints.

Check a misconception first · Try a connected problem

Read an original example question

The lines have equations y = 5x + 3 and 2y = 10x + 10. A student says that they meet because the coefficients of x differ.

Part a

Find the gradient of the second line.

Part b

State the relationship between the two lines.

Part c

Explain the error in the student’s argument.

Model solution and review criteria

Part a

Divide every term of its equation by 2. The gradient is 5.

Divide the entire equation, including its constant.
Identify the coefficient of x as the gradient.

Part b

Their gradients agree but their intercepts differ.

Compare gradients and intercepts.

Part c

Raw coefficients cannot be compared before the equations use the same form. Equal gradients and different intercepts prevent an intersection.

Put both equations in a comparable form.
Connect gradient and intercept to the geometric conclusion.

Compare your own reasoning. No automatic examination marks are awarded.