Lesson Plan

• Describe the gradient, slope‑intercept and standard forms of a straight line.
• Apply formulas to find intersections, mid‑points, distances and circle parameters.
• Solve problems involving parallel and perpendicular lines using algebraic methods.
• Interpret geometric results and verify solutions through calculation.

• Whiteboard and markers
• Projector with slide deck of formulas and diagrams
• Graph paper and rulers
• Worksheet with practice questions
• Calculator (optional)

Begin with a quick visual of two intersecting streets to show how knowing slopes helps us navigate. Review the gradient concept from previous lessons and state that today students will master using line equations to solve real‑world geometry problems. Success criteria: students will correctly derive and manipulate line and circle equations and verify their answers.

1. Do‑Now (5'): Quick worksheet on identifying gradients from plotted points.
2. Mini‑lecture (15'): Introduce/recap line forms, parallel‑perpendicular conditions, and circle equations with examples on the projector.
3. Guided Example (10'): Work through the provided A‑B line and intersection problem, modelling each algebraic step.
4. Pair Activity (15'): Students solve a set of practice questions (mid‑point, distance, circle centre/radius, parallel line).
5. Class Discussion & Check (10'): Review answers, address misconceptions, and highlight common errors.
6. Exit Ticket (5'): Each student writes one solved problem and the key formula used.

Summarise how the different forms of line equations interrelate and how they enable us to find intersections, mid‑points and circle properties. Collect exit tickets as a quick retrieval check. For homework, assign three mixed problems requiring the use of at least two different formulae from today’s lesson.