This deep dive covers Special Cases and Variations 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 9 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Special Cases and Variations
| Equation Type | Form | Special Property |
|---|---|---|
| Through origin | y = mx | c = 0, passes through (0, 0) |
| Horizontal line | y = c | m = 0, parallel to x-axis |
| Steep positive | y = 5x + c | Large positive gradient |
| Gentle negative | y = -0.5x + c | Small negative gradient |
| 45° line | y = x + c | m = 1, rises 1 for every 1 across |
Practice questions for y = mx + c
For the line y = 3x – 2, what is the gradient?
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.
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)