• 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 (−3, 3) with slope −2? (y + 3 = −2(x − 3) / y − 3 = 2(x + 3) / y − 3 = −2(x + 3) / x + 3 = −2(y − 3)) → y − 3 = −2(x + 3)Prompt: Point-slope form: y − y₁ = m(x − x₁).
2. Write y + 5 = −2(x − 2) in the form y = mx + b. Type the right-hand side. → -2x-1Prompt: Expand the bracket first.
3. Noah's phone plan costs 2 more for each extra gigabyte of data. A month with 4 GB costs 16. Using cost = m × GB + b, find b, the fixed monthly charge. → 8Prompt: The slope m is the cost per gigabyte.

• 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.

• 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.

• 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 (−3, −2) and (0, −3). Type the right-hand side of y = … (fractions are fine). → -(1/3)x-3Prompt: The slope will be a fraction this time.
2. A line passes through (−4, −5) and (4, 3). The point (−1, k) is also on the line. Find k. → -2Prompt: Find the equation of the line first.

• 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.

• 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 (4, −4) and (−4, 0). Type the right-hand side of y = … (fractions are fine). → -(1/2)x-2Prompt: The slope will be a fraction this time.
2. A line passes through (−4, 8) and (4, −16). The point (−1, k) is also on the line. Find k. → -1Prompt: Find the equation of the line first.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.