📚 Part 1: Coordinate Foundations & Gradient Classification

1. For the point P(−3, 4):

a) State the x-coordinate: ________

b) State the y-coordinate: ________

2. Identify the quadrant for each point (I, II, III or IV):

a) A(2, 5) b) B(−4, 3) c) C(−2, −6) d) D(3, −1)

3. Which axis contains the point E(0, −2)?

4. Classify the gradient of each described line. Choose: Positive / Negative / Zero / Undefined

4a) Line through (1,1) and (4,4)

Positive

Negative

Zero

Undefined

4b) Horizontal line y = 2

Positive

Negative

Zero

Undefined

4c) Vertical line x = −3

Positive

Negative

Zero

Undefined

✏️ Part 2: Calculate Gradients and y‑Intercepts

For each question show the signed rise, the run and the simplified gradient (rise over run). Then state the y‑intercept as an ordered pair.

5. Line L1 passes through A(1, 2) and B(4, 5).

y‑intercept of L1: ____________

6. Line L2 passes through C(−2, 3) and D(2, −1).

y‑intercept of L2: ____________

7. Line L3 is vertical and passes through x = 3. Explain the gradient and give the y‑intercept if any.

8. Sketch (roughly) the line passing through E(0, −2) with gradient 2. On your sketch indicate one rise/run triangle.

🔍 Part 3: Extension — Reasoning

9. A student says a vertical line has gradient 0. Explain the error in one or two sentences.

10. Line A: rises 6 and runs 3. Line B: rises 4 and runs 2. Compare the gradients and state what this suggests about the two lines.

11. A line passes through F(2, 1) and G(5, 7). Find its gradient and y‑intercept. Show working (rise, run, simplify) and state the y‑intercept as an ordered pair.

Gradient and Graphs Worksheet

Gradient and Graphs Worksheet

📚 Part 1: Coordinate Foundations & Gradient Classification

✏️ Part 2: Calculate Gradients and y‑Intercepts

🔍 Part 3: Extension — Reasoning

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