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Math lesson plan · 9th grade (Year 10 in England) · 45 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 · 5 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.
  1. A line has slope 5 and crosses the y-axis at 0. Write its equation as y = … (type the right-hand side). → 5xPrompt: Use y = mx + b.
  2. Find the equation of the line through (0, 0) and (2, 2). Type the right-hand side of y = … . → xPrompt: Find the slope first.
  3. A line has slope 3 and crosses the y-axis at −8. Write its equation as y = … (type the right-hand side). → 3x-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: Use point-slope form y − y₁ = m(x − x₁). 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: 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 · 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.
  1. Which equation is the line through (2, −4) with slope −5? (y + 4 = −5(x − 2) / y + 4 = 5(x − 2) / y − 4 = −5(x + 2) / y − 2 = −5(x + 4)) → y + 4 = −5(x − 2)Prompt: Point-slope form: y − y₁ = m(x − x₁).
  2. Write y − 5 = (x + 6) in the form y = mx + b. Type the right-hand side. → x+11Prompt: Expand the bracket 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.
  1. Which equation is the line through (−1, 4) with slope −3? (y − 4 = −3(x + 1) / y + 1 = −3(x − 4) / x + 1 = −3(y − 4) / y + 4 = −3(x − 1)) → y − 4 = −3(x + 1)Prompt: Point-slope form: y − y₁ = m(x − x₁).
  2. Write y − 1 = −2(x + 6) in the form y = mx + b. Type the right-hand side. → -2x-11Prompt: Expand the bracket 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: 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

eurekami

Use point-slope form y − y₁ = m(x − x₁)

Name

Date

Score/ 8

  1. Question 1

    Kai's phone plan costs 5 more for each extra gigabyte of data. A month with 8 GB costs 59. Using cost = m × GB + b, find b, the fixed monthly charge.

    Answer

  2. Question 2

    Write y + 1 = 4(x + 5) in the form y = mx + b. Type the right-hand side.

    Answer

  3. Question 3

    Which equation is the line through (5, 3) with slope −3?

    • A. y − 3 = 3(x − 5)
    • B. y − 3 = −3(x − 5)
    • C. y − 5 = −3(x − 3)
    • D. x − 5 = −3(y − 3)

  4. Question 4

    Diego's phone plan costs 6 more for each extra gigabyte of data. A month with 10 GB costs 68. Using cost = m × GB + b, find b, the fixed monthly charge.

    Answer

  5. Question 5

    Write y − 3 = −(x − 6) in the form y = mx + b. Type the right-hand side.

    Answer

  6. Question 6

    Which equation is the line through (−6, 4) with slope −4?

    • A. y + 4 = −4(x − 6)
    • B. y − 4 = 4(x + 6)
    • C. y + 6 = −4(x − 4)
    • D. y − 4 = −4(x + 6)

  7. Question 7

    Kai's phone plan costs 3 more for each extra gigabyte of data. A month with 10 GB costs 46. Using cost = m × GB + b, find b, the fixed monthly charge.

    Answer

  8. Question 8

    Write y − 1 = −2(x − 3) in the form y = mx + b. Type the right-hand side.

    Answer

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Answer key: Use point-slope form y − y₁ = m(x − x₁)

  1. 1. 19

  2. 2. 4x+19

  3. 3. B. y − 3 = −3(x − 5)

  4. 4. 8

  5. 5. -x+9

  6. 6. D. y − 4 = −4(x + 6)

  7. 7. 16

  8. 8. -2x+7