• Quick retrieval from earlier learning (Write y = mx + b from a slope and intercept, or from a graph). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Write the equation of the line with slope −6 and y-intercept −10. Type the right-hand side (y = …). → -6x-10Prompt: Use y = mx + b.
2. Grace says the line through (0, −5) with slope 5 is y = −5x + 5. Write the correct equation. Type the right-hand side. → 5x-5Prompt: Grace swapped the slope and the intercept.
3. Write the equation of the line with slope −5 and y-intercept −5. Type the right-hand side (y = …). → -5x-5Prompt: Use y = mx + b.

• Show a "think of a number" puzzle and ask the class to work out the starting number.
• Share the objective: Interpret rate of change and initial value in context. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A bamboo shoot is 10 cm tall and grows 10 cm per day. In y = mx + b, what is b?
• Step 1: b = 10
• Step 2: y = 10x + 10
• Answer: 10
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A bamboo shoot is 34 cm tall and grows 5 cm per day. In y = mx + b, what is m? → 5Prompt: m is the rate of change: how much per unit of time.
2. A water tank holds 67 litres and drains at 7 litres per minute. Write the amount left after t minutes and find how much is left after 2 minutes. → 53Prompt: The rate of change is −7 (it goes down).

• 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.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. The cost of a pottery class is C = 9h + 29, where h is hours. What does 29 represent? (The cost per hour / A fixed fee paid even for 0 hours / The number of hours / The total cost for 29 hours) → A fixed fee paid even for 0 hoursPrompt: Which number is multiplied by h?
2. A video has 29 likes and gains 12 likes per minute. In y = mx + b, what is m? → 12Prompt: m is the rate of change: how much per unit of time.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.