GCSE Maths Straight-Line Graphs (y = mx + c) Notes
Every straight line has the equation y = mx + c, where m is the gradient (steepness) and c is where the line crosses the y-axis.
Key concepts
- Gradient (m)
- How steep the line is — the change in y divided by the change in x. Positive slopes up, negative slopes down.
- y-intercept (c)
- The value of y where the line crosses the y-axis (when x = 0).
- Parallel lines
- Lines with the same gradient m never meet — only c differs.
- Reading the equation
- Rearrange to y = mx + c to read off m and c directly.
Key formulas
Equation of a line
y = mx + c
Gradient between two points
m = (y₂ − y₁) ÷ (x₂ − x₁)
Worked example
Find the gradient and y-intercept of the line through (0, 1) and (2, 7).
- 1Gradient m = (7 − 1) ÷ (2 − 0) = 6 ÷ 2 = 3.
- 2The line passes through (0, 1), so c = 1.
- 3Write the equation: y = 3x + 1.
Answer: Gradient 3, y-intercept 1, so y = 3x + 1
Common mistakes
✗ Mixing up gradient and intercept in y = mx + c.
✓ m is the number in front of x; c is the number on its own.
✗ Getting the gradient upside down.
✓ It is change in y over change in x — vertical divided by horizontal.
✗ Forgetting negative gradients slope downwards.
✓ A line falling left to right has a negative gradient.
Quick check
Try these, then reveal the answers.
State the gradient of y = 4x − 2.Reveal answer
4
Where does y = 2x + 5 cross the y-axis?Reveal answer
At (0, 5).
Are y = 3x + 1 and y = 3x − 4 parallel?Reveal answer
Yes — same gradient.
Exam tips
- Always rearrange to y = mx + c before reading off m and c.
- To draw a line, plot the y-intercept then use the gradient to find a second point.
- Parallel lines share the same gradient; use that to find a missing equation.
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Frequently asked questions
What do m and c mean in y = mx + c?+
m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
How do I find the gradient from two points?+
Divide the difference in the y-values by the difference in the x-values.
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