Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Use point-slope form y − y₁ = m(x − x₁)
Algebra
CCSS HSA.CED.A.2CCSS HSF.LE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Use point-slope form y − y₁ = m(x − x₁).
- 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: Find the equation of a line
Leads to: Write the equation of a line from two points
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Find the equation of a line). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A line has slope −2 and crosses the y-axis at −4. Write its equation as y = … (type the right-hand side). → -2x-4Prompt: Use y = mx + b.
- Find the equation of the line through (1, 10) and (5, 26). Type the right-hand side of y = … . → 4x+6Prompt: Find the slope first.
- A line has slope −1 and crosses the y-axis at 4. Write its equation as y = … (type the right-hand side). → -x+4Prompt: Use y = mx + b.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Use point-slope form y − y₁ = m(x − x₁). Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Which equation is the line through (4, −1) with slope 1?
- Step 1: y + 1 = (x − 4)
- Answer: y + 1 = (x − 4)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Which equation is the line through (1, −6) with slope −2? (y − 6 = −2(x + 1) / x − 1 = −2(y + 6) / y − 1 = −2(x + 6) / y + 6 = −2(x − 1)) → y + 6 = −2(x − 1)Prompt: Point-slope form: y − y₁ = m(x − x₁).
- Write y + 2 = 3(x − 1) in the form y = mx + b. Type the right-hand side. → 3x-5Prompt: Expand the bracket first.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write y + 1 = 2(x − 4) in the form y = mx + b. Type the right-hand side. → 2x-9Prompt: Expand the bracket first.
- Lucia's phone plan costs 5 more for each extra gigabyte of data. A month with 6 GB costs 47. Using cost = m × GB + b, find b, the fixed monthly charge. → 17Prompt: The slope m is the cost per gigabyte.
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: Find the equation of a line.
- 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
- Move on to: Write the equation of a line from two points.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder