Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Write the equation of a line from two points
Algebra
CCSS HSF.LE.A.2CCSS HSA.CED.A.2England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Write the equation of a line from 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: Use point-slope form y − y₁ = m(x − x₁)
Leads to: Write the equation of a parallel line through a point
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 (Use point-slope form y − y₁ = m(x − x₁)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which equation is the line through (1, −1) with slope 3? (y + 1 = −3(x − 1) / y − 1 = 3(x + 1) / x − 1 = 3(y + 1) / y + 1 = 3(x − 1)) → y + 1 = 3(x − 1)Prompt: Point-slope form: y − y₁ = m(x − x₁).
- Write y − 5 = 3(x + 4) in the form y = mx + b. Type the right-hand side. → 3x+17Prompt: Expand the bracket first.
- Zoe's phone plan costs 6 more for each extra gigabyte of data. A month with 11 GB costs 90. Using cost = m × GB + b, find b, the fixed monthly charge. → 24Prompt: The slope m is the cost per gigabyte.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Write the equation of a line from 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 (−3, −5) and (3, −1). Type the right-hand side of y = … (fractions are fine).
- Step 1: m = 4/6 = 2/3
- Step 2: y = (2/3)x − 3
- Answer: (2/3)x-3
- 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 (6, 2) and (3, 1). Type the right-hand side of y = … (fractions are fine). → (1/3)xPrompt: The slope will be a fraction this time.
- A line passes through (−3, 12) and (1, 4). The point (4, k) is also on the line. Find k. → -2Prompt: Find the equation of the line first.
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.
- Find the equation of the line through (0, 5) and (−3, 3). Type the right-hand side of y = … (fractions are fine). → (2/3)x+5Prompt: The slope will be a fraction this time.
- A line passes through (3, −15) and (4, −18). The point (2, k) is also on the line. Find k. → -12Prompt: Find the equation of the line 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: Use point-slope form y − y₁ = m(x − x₁).
- 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 parallel line through a point.
- 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