This study notes covers Worked Examples within Linear Graphs Problems for GCSE Mathematics. Revise Linear Graphs Problems in Graphs for GCSE Mathematics with 16 exam-style questions and 11 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 8 of 10 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 10
Practice
16 questions
Recall
11 flashcards
✏️ Worked Examples
Example 1: Interpreting a Real-Life Linear Graph
Question: A mobile phone plan costs £15 per month plus 5p per minute of calls. Write an equation for the total monthly cost C (in £) in terms of minutes m. How much does it cost to make 200 minutes of calls?
Show Solution
Step 1: Identify m and c from the context
Fixed monthly fee (y-intercept): c = 15
Cost per minute (gradient): m = 0.05 (= 5p = £0.05)
Step 2: Write the equation — C = 0.05m + 15
Step 3: Substitute m = 200 — C = 0.05 × 200 + 15 = 10 + 15 = £25
Answer: C = 0.05m + 15. For 200 minutes: £25
Example 2: Solving Simultaneous Equations Graphically
Question: By drawing both lines, solve simultaneously: y = 2x + 1 and y = -x + 7.
Show Solution
Step 1: Plot y = 2x + 1 — three points: (0, 1), (1, 3), (2, 5)
Step 2: Plot y = -x + 7 — three points: (0, 7), (2, 5), (4, 3)
Step 3: Find the intersection — both lines pass through (2, 5).
Check: Line 1: 2(2) + 1 = 5 ✓ Line 2: -(2) + 7 = 5 ✓
Answer: x = 2, y = 5
Example 3: Finding the Equation from Two Points in Context
Question: A car is travelling at constant speed. After 1 hour it is 80 km from home; after 3 hours it is 200 km from home. Write an equation for distance d (km) in terms of time t (hours). How far will it be after 5 hours?
Show Solution
Step 1: Calculate the gradient (speed) — m = (200 - 80) ÷ (3 - 1) = 120 ÷ 2 = 60 km/h
Step 2: Find c (starting distance) — using (1, 80): 80 = 60(1) + c → c = 20
Step 3: Write the equation — d = 60t + 20
Step 4: Substitute t = 5 — d = 60(5) + 20 = 300 + 20 = 320 km
Answer: d = 60t + 20. After 5 hours: 320 km from home