Knowledge Organiser: y = mx + c
Part of y = mx + c · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: y = mx + c 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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
10 questions
Recall
20 flashcards
Knowledge Organiser: y = mx + c
Key Terms
- m (gradient): Controls how steep the line is; positive = upward slope
- c (y-intercept): The value of y when x = 0; where the line crosses the y-axis
- Coefficient: The number multiplying a variable (m is the coefficient of x)
- Rearranging: Rewriting an equation to isolate y on the left-hand side
- Substitution: Replacing a letter with a number to find a coordinate
Must-Know Facts
- In y = mx + c, m is the gradient and c is the y-intercept — read them off directly
- If the equation is not in this form, rearrange to get y on its own first
- Two lines with the same m are parallel (different c, different y-intercepts)
- To find y given x: substitute x into y = mx + c
- To find c from a point: substitute the point into y = mx + c and solve
- Lines through the origin have c = 0, written as y = mx
Key Formulas
- Standard form: y = mx + c
- Gradient from two points: m = (y₂ − y₁) ÷ (x₂ − x₁)
- Find c: substitute known m and a point (x, y) into y = mx + c, then solve for c
- To rearrange ax + by = d into y = mx + c: subtract ax, then divide everything by b
Common Mistakes
- m and c confusion: In y = 3x + 5, m = 3 (gradient) and c = 5 (y-intercept) — don't swap them
- Rearranging with negative b: For 2x − 3y = 6, rearranging gives y = ⅔x − 2 — divide ALL terms by the coefficient of y, including sign
- Finding c after finding m: Substitute a known point AND m into y = mx + c, then solve for c — don't assume c = y-value of the point
- Gradient from ax + by = c form: Rearrange to y = mx + c form first before reading off m
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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
10 questions on y = mx + c — practise free
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