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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Write y = mx + b from a slope and intercept, or from a graph

Algebra

CCSS 8.F.B.4CCSS 8.EE.B.6England: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Write y = mx + b from a slope and intercept, or from a graph.

  • 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 y-intercept from an equation, table or graph; Find the slope from a graph using rise over run

Leads to: Find the equation of a line through two points; Rearrange ax + by = c to find slope and intercept; Interpret rate of change and initial value in context

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 y-intercept from an equation, table or graph; Find the slope from a graph using rise over run). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What is the y-intercept of y = −5x − 1? → -1Prompt: The y-intercept is the value of y when x = 0.
  2. x: 1, 2, 3, 4. y: −3, 1, 5, 9. The pattern is linear. What is the y-intercept? → -7Prompt: Work out how much y changes when x goes up by 1.
  3. What is the y-intercept of y = −11 − 3x? → -11Prompt: The y-intercept is the value of y when x = 0.

Hook · 3 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Write y = mx + b from a slope and intercept, or from a graph. 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: Write the equation of the line with slope −5 and y-intercept 5. Type the right-hand side (y = …).
  • Step 1: y = −5x + 5
  • Answer: -5x+5
  • 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.
  1. Write the equation of the line with slope 2 and y-intercept −8. Type the right-hand side (y = …). → 2x-8Prompt: Use y = mx + b.
  2. Ethan says the line through (0, 1) with slope 3 is y = x + 3. Write the correct equation. Type the right-hand side. → 3x+1Prompt: Ethan swapped the slope and the intercept.

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.
  1. Write the equation of the line with slope 2 and y-intercept 5. Type the right-hand side (y = …). → 2x+5Prompt: Use y = mx + b.
  2. Zoe says the line through (0, −2) with slope −5 is y = −2x − 5. Write the correct equation. Type the right-hand side. → -5x-2Prompt: Zoe swapped the slope and the intercept.

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 y-intercept from an equation, table or graph.
  • 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: Find the equation of a line through two points; Rearrange ax + by = c to find slope and intercept; Interpret rate of change and initial value in context.
  • 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-8.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Write y = mx + b from a slope and intercept, or from a graph

Name

Date

Score/ 6

  1. Question 1

    Write the equation of the line shown. Type the right-hand side (y = …).

    xy−66−12−66120y = x − 1(0, −1)(1, 0)

    Answer

  2. Question 2

    Felix says the line through (0, 5) with slope 1 is y = 5x + 1. Write the correct equation. Type the right-hand side.

    Answer

  3. Question 3

    Write the equation of the line with slope 7 and y-intercept 4. Type the right-hand side (y = …).

    Answer

  4. Question 4

    Amara says the line through (0, 5) with slope −4 is y = 5x − 4. Write the correct equation. Type the right-hand side.

    Answer

  5. Question 5

    Write the equation of the line with slope −5 and y-intercept −6. Type the right-hand side (y = …).

    Answer

  6. Question 6

    Daniel says the line through (0, 5) with slope −1 is y = 5x − 1. Write the correct equation. Type the right-hand side.

    Answer

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Answer key: Write y = mx + b from a slope and intercept, or from a graph

  1. 1. x-1

  2. 2. x+5

  3. 3. 7x+4

  4. 4. -4x+5

  5. 5. -5x-6

  6. 6. -x+5