Module 9 of 30Lesson 1 of 14 · CG-C1 Drawing Linear Graphs
Coordinate Geometry strand · Unit CG-C1 · Syllabus C3.1 & C3.2

Drawing Linear Graphs

🔵 Core levely = mx + c, drawn to exam standard

1 Learn it

Exam questions hand you an equation like \(y = -2x + 5\) and a grid. The professional routine:

🔑 1️⃣ Build a small table (three x-values including 0). 2️⃣ Plot with small neat crosses. 3️⃣ Ruler through all three, EXTENDING across the full grid — a too-short line loses a mark.

For \(y = -2x + 5\): x = 0 → 5, x = 1 → 3, x = 3 → −1. The negative multiplier makes it fall left-to-right — predict the direction before plotting; prediction catches table errors instantly.

The +c tells you where it cuts the y-axis. Positive slope climbs, negative slope falls.

2 Watch it work
EXAMPLE 1

Draw \(y = -2x + 5\) (the syllabus’s example).

Table: (0, 5), (1, 3), (3, −1). Falling line cutting the y-axis at 5.

EXAMPLE 2

Draw \(y = \tfrac{1}{2}x + 1\).

Use EVEN x-values to dodge fractions: (0, 1), (2, 2), (4, 3). A gentle climb.

EXAMPLE 3

Where does \(y = -2x + 5\) cross the axes?

y-axis: (0, 5). x-axis: 0 = −2x + 5 → x = 2.5 → (2.5, 0).

EXAMPLE 4

Two lines on one grid solve simultaneous equations.

Where y = −2x + 5 meets y = x − 1: the crossing (2, 1). Check: −4 + 5 = 1 ✔ — graphs and A-C6 agree.

3 Your turn — try first, then reveal
🚫 No calculator[2 marks]

Q1. Complete the table for \(y = -2x + 5\): x = 0, 2, 4.

👀 Show answer
✍️ How your working should look in the exam
y = 5, 1, −3   ✓ B2
Why this works
Each 2-step in x drops y by 4 — the −2 acting twice.

🚫 No calculator[1 mark]

Q2. Without plotting, does \(y = 3x – 2\) climb or fall, left to right?

👀 Show answer
✍️ How your working should look in the exam
climbs (positive gradient 3)   ✓ B1
Why this works
The sign of the x-multiplier decides direction before any table exists.

🚫 No calculator[2 marks]

Q3. Where does \(y = 3x – 2\) cross each axis?

👀 Show answer
✍️ How your working should look in the exam
y-axis: (0, −2)   ✓ B1
x-axis: 3x = 2 → (23, 0)   ✓ B1
Why this works
x = 0 for the y-crossing; y = 0 for the x-crossing. Fractions welcome.

🚫 No calculator[1 mark]

Q4. Why choose x = 0, 2, 4 when drawing \(y = \tfrac{1}{2}x + 1\)?

👀 Show answer
✍️ How your working should look in the exam
even x-values give whole-number y-values   ✓ B1
Why this works
Halving evens lands on integers — exact plots, fewer slips.

🚫 No calculator[2 marks]

Q5. Lines \(y = -2x + 5\) and \(y = x – 1\) cross at (2, 1). What does that point tell you?

👀 Show answer
✍️ How your working should look in the exam
x = 2, y = 1 satisfies BOTH equations at once   ✓ B2
Why this works
A crossing point obeys both rules — the graphical face of simultaneous equations.

4 Common mistakes — don’t lose easy marks
  • Line too short: extend across the whole grid.
  • Sign slips on negative gradients: y = −2x + 5 at x = 3 is −1, not 11.
  • Blobs instead of crosses: small neat crosses locate points precisely.
  • Odd x-values with fraction gradients: pick values the fraction divides cleanly.
5 How the exam asks this

“Draw the graph of y = … for −2 ⩽ x ⩽ 4” earns 2–3 marks on Papers 1 and 3, usually with a follow-up read-off. Next: measuring steepness — the gradient.

✅ Take the Check Yourself quiz below, then continue to CG-C2 Gradient.

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