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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.
  1. Which equation is the line through (5, −3) with slope 3? (y − 3 = 3(x + 5) / y − 5 = 3(x + 3) / y + 3 = 3(x − 5) / x − 5 = 3(y + 3)) → y + 3 = 3(x − 5)Prompt: Point-slope form: y − y₁ = m(x − x₁).
  2. Write y − 6 = −2(x − 5) in the form y = mx + b. Type the right-hand side. → -2x+16Prompt: Expand the bracket first.
  3. Nia's phone plan costs 3 more for each extra gigabyte of data. A month with 9 GB costs 32. Using cost = m × GB + b, find b, the fixed monthly charge. → 5Prompt: 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.
  1. Find the equation of the line through (4, 1) and (−4, 5). Type the right-hand side of y = … (fractions are fine). → -(1/2)x+3Prompt: The slope will be a fraction this time.
  2. A line passes through (3, −13) and (−5, 11). The point (0, k) is also on the line. Find k. → -4Prompt: 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.
  1. Find the equation of the line through (−3, −3) and (0, −5). Type the right-hand side of y = … (fractions are fine). → -(2/3)x-5Prompt: The slope will be a fraction this time.
  2. A line passes through (−5, −14) and (−4, −11). The point (5, k) is also on the line. Find k. → 16Prompt: 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

eurekami

Write the equation of a line from two points

Name

Date

Score/ 8

  1. Question 1

    Find the equation of the line through (4, 3) and (−2, 6). Type the right-hand side of y = … (fractions are fine).

    Answer

  2. Question 2

    A line passes through (3, −13) and (5, −19). The point (4, k) is also on the line. Find k.

    Answer

  3. Question 3

    Find the equation of the line through (−3, −5) and (0, 4). Type y = … (just the right-hand side).

    xy−6−4−2246−15150(−3, −5)(0, 4)

    Answer

  4. Question 4

    Find the equation of the line through (6, −5) and (3, −3). Type the right-hand side of y = … (fractions are fine).

    Answer

  5. Question 5

    A line passes through (0, 1) and (−2, −7). The point (2, k) is also on the line. Find k.

    Answer

  6. Question 6

    Find the equation of the line through (−3, 1) and (−4, 2). Type y = … (just the right-hand side).

    xy−6−4−2246−15150(−3, 1)(−4, 2)

    Answer

  7. Question 7

    Find the equation of the line through (−6, −3) and (6, 5). Type the right-hand side of y = … (fractions are fine).

    Answer

  8. Question 8

    A line passes through (3, −7) and (−5, 25). The point (2, k) is also on the line. Find k.

    Answer

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Answer key: Write the equation of a line from two points

  1. 1. -(1/2)x+5

  2. 2. -16

  3. 3. 3x+4

  4. 4. -(2/3)x-1

  5. 5. 9

  6. 6. -x-2

  7. 7. (2/3)x+1

  8. 8. -3