• 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 −7 and y-intercept 6. Type the right-hand side (y = …). → -7x+6Prompt: Use y = mx + b.
2. Grace says the line through (0, −1) with slope −2 is y = −x − 2. Write the correct equation. Type the right-hand side. → -2x-1Prompt: Grace swapped the slope and the intercept.
3. Write the equation of the line with slope −5 and y-intercept 9. Type the right-hand side (y = …). → -5x+9Prompt: 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 video has 33 likes and gains 2 likes per minute. In y = mx + b, what is b? → 33Prompt: m is the rate of change: how much per unit of time.
2. A water tank holds 69 litres and drains at 8 litres per minute. Write the amount left after t minutes and find how much is left after 6 minutes. → 21Prompt: The rate of change is −8 (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 = 2h + 28, where h is hours. What does 28 represent? (The number of hours / The cost per hour / A fixed fee paid even for 0 hours / The total cost for 28 hours) → A fixed fee paid even for 0 hoursPrompt: Which number is multiplied by h?
2. A water tank holds 49 litres and drains at 6 litres per minute. Write the amount left after t minutes and find how much is left after 5 minutes. → 19Prompt: The rate of change is −6 (it goes down).

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