Module 8 of 30Lesson 1 of 2 · CG-F1 Plotting Straight Lines
Coordinate Geometry strand · Unit CG-F1 · Builds towards C3.2

Plotting Straight Lines

🟢 Foundation levelFrom rule to ruler

1 Learn it

A-F7 taught you to read coordinates. Now you’ll CREATE lines: every equation like \(y = 2x + 1\) describes a family of points, and plotting three of them (two plus a checker) reveals a perfect straight line.

🔑 Three-point recipe: pick easy x-values (0, 1, 2 or 0, 2, 4), compute each y from the rule, plot the three points, and join with a RULER through all three. If the third point misses the line, one calculation is wrong — that is exactly why we plot three, not two.

For \(y = 2x + 1\): x = 0 → y = 1 · x = 1 → y = 3 · x = 2 → y = 5. Points (0,1), (1,3), (2,5) — one straight line through all of them.

Special lines worth knowing on sight: \(y = 3\) is a HORIZONTAL line through 3 on the y-axis; \(x = 2\) is a VERTICAL line through 2 on the x-axis.

2 Watch it work
EXAMPLE 1

Make a table for \(y = x + 2\) using x = 0, 1, 2.

y-values: 2, 3, 4 → points (0,2), (1,3), (2,4).

EXAMPLE 2

Make a table for \(y = 2x – 1\) using x = 0, 1, 3.

y: −1, 1, 5 → the line climbs 2 for every 1 across — steeper than y = x + 2.

EXAMPLE 3

Which line is y = 3 — and which is x = 3?

y = 3: every point has height 3 → horizontal. x = 3: every point stands at 3 across → vertical.

EXAMPLE 4

Does the point (4, 9) lie on \(y = 2x + 1\)?

2(4) + 1 = 9 ✔ — yes. A point lies on a line when its coordinates OBEY the rule.

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

Q1. Complete the table for \(y = x + 3\): x = 0, 2, 4.

👀 Show answer
✍️ How your working should look in the exam
y = 3, 5, 7   ✓ B2
Why this works
Add 3 to each x. Three points ready for plotting.

🚫 No calculator[1 mark]

Q2. Which point does EVERY line of the form y = mx pass through?

👀 Show answer
✍️ How your working should look in the exam
the origin (0, 0)   ✓ B1
Why this works
x = 0 gives y = 0 whatever m is — no +c means no lift.

🚫 No calculator[1 mark]

Q3. Describe the line \(x = -2\).

👀 Show answer
✍️ How your working should look in the exam
a vertical line through −2 on the x-axis   ✓ B1
Why this works
Every point on it is 2 to the LEFT, at any height.

🚫 No calculator[2 marks]

Q4. Does (5, 8) lie on the line \(y = 2x – 1\)? Show how you decide.

👀 Show answer
✍️ How your working should look in the exam
2(5) − 1 = 9 ≠ 8   ✓ M1
no — the point is not on the line   ✓ A1
Why this works
Substitute x = 5; the rule delivers 9, not 8. Obey-the-rule is the whole test.

🚫 No calculator[2 marks]

Q5. Two lines: \(y = x\) and \(y = 3x\). Which is steeper, and where do they cross?

👀 Show answer
✍️ How your working should look in the exam
y = 3x is steeper   ✓ B1 — they cross at (0, 0)   ✓ B1
Why this works
Bigger number in front of x = steeper climb; both pass through the origin.

4 Common mistakes — don’t lose easy marks
  • Plotting only two points: the third is your error-detector.
  • x = 3 and y = 3 swapped: x = k is vertical, y = k is horizontal.
  • Freehand “straight” lines: use a ruler — wobbles cost the accuracy mark.
  • Table slips with negatives: y = 2x − 1 at x = 0 is −1, not 1.
5 Where this leads

Core unit CG-C1 draws these lines at exam speed, CG-C2 measures their steepness (the gradient), and CG-C3 reads the equation OFF a drawn line. Everything in this strand grows from today’s three-point recipe.

✅ Take the Check Yourself quiz below, then continue to CG-C1.

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