This deep dive covers Worked Examples within y = mx + c for GCSE Mathematics. Revise y = mx + c in Graphs for GCSE Mathematics with 10 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 9
Practice
10 questions
Recall
20 flashcards
Worked Examples
Example 1: Interpreting y = -2x + 8
What can we tell about this line?
- Gradient m = -2 (negative, so slopes downward)
- Y-intercept c = 8 (crosses y-axis at (0, 8))
- For every 1 unit right, line goes 2 units down
- X-intercept: Set y = 0: 0 = -2x + 8, so x = 4
Example 2: Finding Equation from Points
Find equation of line through (1, 5) and (3, 11)
Solution:
- Gradient: m = (11 - 5)/(3 - 1) = 6/2 = 3
- Using point (1, 5): 5 = 3(1) + c
- So: 5 = 3 + c, therefore c = 2
- Equation: y = 3x + 2
Example 3: Real-world Application
A plumber charges £40 call-out fee plus £25 per hour. Write the cost equation.
Solution:
- Fixed cost (c) = £40
- Hourly rate (m) = £25 per hour
- If C = total cost and t = time in hours
- Equation: C = 25t + 40