GraphsDeep Dive

Worked Examples

Part of y = mx + cGCSE Mathematics

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:

  1. Gradient: m = (11 - 5)/(3 - 1) = 6/2 = 3
  2. Using point (1, 5): 5 = 3(1) + c
  3. So: 5 = 3 + c, therefore c = 2
  4. 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

Keep building this topic

Read this section alongside the surrounding pages in y = mx + c. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for y = mx + c

For the line y = 3x – 2, what is the gradient?

  • A. –2
  • B. 3
  • C. 2
  • D. –3
1 markfoundation

Two students write down equations for parallel lines: Student A writes: y = 2x + 1 Student B writes: y = 2x + 1 Explain why these two lines are NOT parallel to each other.

2 markshigher

Quick Recall Flashcards

What is special about y = mx?
It passes through the origin (0, 0) because c = 0.
What gradient gives a 45° line?
m = 1 (rises 1 unit for every 1 unit across)

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