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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Write the equation of a parallel line through a point

Algebra

CCSS HSG.GPE.B.5England: GCSE Higher Algebra

Objective and success criteria

Students will: Write the equation of a parallel line through a point.

  • 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 the equation of a line from two points

Leads to: Write the equation of a perpendicular 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 (Write the equation of a line from two points). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Find the equation of the line through (6, 5) and (−3, −1). Type the right-hand side of y = … (fractions are fine). → (2/3)x+1Prompt: The slope will be a fraction this time.
  2. A line passes through (3, −1) and (−3, 5). The point (−4, k) is also on the line. Find k. → 6Prompt: Find the equation of the line first.
  3. Find the equation of the line through (−2, −4) 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.

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 parallel line through a point. 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 line parallel to −3x − y = −1 through (−1, 6). Type the right-hand side of y = … .
  • Step 1: m = −3
  • Step 2: b = 6 − −3 × (−1) = 3
  • Step 3: y = −3x + 3
  • Answer: -3x+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 line parallel to 12x + 4y = −4 through (−1, 6). Type the right-hand side of y = … . → -3x+3Prompt: Rearrange the given line into y = mx + b to read its slope.
  2. Find the line parallel to −2x − 2y = −2 through (−4, 4). Type the right-hand side of y = … . → -xPrompt: Rearrange the given line into y = mx + b to read its slope.

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 line parallel to 4x − 4y = −12 through (3, 4). Type the right-hand side of y = … . → x+1Prompt: Rearrange the given line into y = mx + b to read its slope.
  2. Find the line parallel to 4x − 4y = −4 through (−3, −2). Type the right-hand side of y = … . → x+1Prompt: Rearrange the given line into y = mx + b to read its slope.

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 the equation of a line from two points.
  • 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 perpendicular 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 parallel line through a point

Name

Date

Score/ 8

  1. Question 1

    Find the line parallel to −4x + 4y = −8 through (−3, −6). Type the right-hand side of y = … .

    Answer

  2. Question 2

    Find the line parallel to y = x − 5 that passes through (2, 0). Type the right-hand side of y = … .

    xy−66−12−66120y = x − 5(2, 0)

    Answer

  3. Question 3

    Find the line parallel to 8x + 4y = −8 through (−2, −1). Type the right-hand side of y = … .

    Answer

  4. Question 4

    Find the line parallel to y = 3x + 5 that passes through (−1, −3). Type the right-hand side of y = … .

    xy−66−12−66120y = 3x + 5(−1, −3)

    Answer

  5. Question 5

    Find the line parallel to 2x − y = −3 through (1, −6). Type the right-hand side of y = … .

    Answer

  6. Question 6

    Find the line parallel to y = −4x + 1 that passes through (2, 1). Type the right-hand side of y = … .

    xy−66−12−66120y = −4x + 1(2, 1)

    Answer

  7. Question 7

    Find the line parallel to 8x + 4y = 4 through (3, −4). Type the right-hand side of y = … .

    Answer

  8. Question 8

    Find the line parallel to y = 3x − 2 that passes through (4, 0). Type the right-hand side of y = … .

    xy−66−12−66120y = 3x − 2(4, 0)

    Answer

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Answer key: Write the equation of a parallel line through a point

  1. 1. x-3

  2. 2. x-2

  3. 3. -2x-5

  4. 4. 3x

  5. 5. 2x-8

  6. 6. -4x+9

  7. 7. -2x+2

  8. 8. 3x-12