Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Find the equation of a line through two points
Algebra
CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Find the equation of a line through two points.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Write y = mx + b from a slope and intercept, or from a graph
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Write y = mx + b from a slope and intercept, or from a graph). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write the equation of the line with slope −6 and y-intercept −1. Type the right-hand side (y = …). → -6x-1Prompt: Use y = mx + b.
- Daniel says the line through (0, −2) with slope −5 is y = −2x − 5. Write the correct equation. Type the right-hand side. → -5x-2Prompt: Daniel swapped the slope and the intercept.
- Write the equation of the line with slope −4 and y-intercept −8. Type the right-hand side (y = …). → -4x-8Prompt: Use y = mx + b.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the equation of a line through two points. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the equation of the line through (−1, 3) and (1, 11). Type the right-hand side (y = …).
- Step 1: m = 8 ÷ 2 = 4
- Step 2: 3 = 4 × (−1) + b → b = 7
- Step 3: y = 4x + 7
- Answer: 4x+7
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Find the equation of the line through (2, 12) and (5, 24). Type the right-hand side (y = …). → 4x+4Prompt: Find the slope first.
- A line has slope −1 and passes through (3, −10). What is its y-intercept? → -7Prompt: Substitute x, y and m into y = mx + b.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A line has slope 2 and passes through (5, 3). What is its y-intercept? → -7Prompt: Substitute x, y and m into y = mx + b.
- Find the equation of the line through (−4, 6) and (0, −2). Type the right-hand side (y = …). → -2x-2Prompt: Find the slope first.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Write y = mx + b from a slope and intercept, or from a graph.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder