IGCSE Maths Straight-Line Graphs Notes
Every straight line has the form y = mx + c, where m is the gradient and c is the y-intercept.
Key concepts
- Gradient (m)
- Steepness of the line, found from change in y ÷ change in x.
- y-intercept (c)
- Where the line crosses the y-axis, at x = 0.
- Parallel & perpendicular
- Parallel lines share m; perpendicular gradients multiply to −1.
Key formulas
Line equation
y = mx + c
Gradient
m = (y₂ − y₁) / (x₂ − x₁)
Perpendicular gradient
m₁ × m₂ = −1
Worked example
Find the equation of the line through (0, 3) with gradient 2.
- 1Gradient m = 2.
- 2The y-intercept is 3, so c = 3.
- 3Substitute into y = mx + c.
Answer: y = 2x + 3
Common mistakes
✗ Mixing up gradient and intercept.
✓ In y = mx + c, m multiplies x, c is the constant.
✗ Wrong sign on the gradient.
✓ A line going down left-to-right has a negative gradient.
✗ Using m for a perpendicular line.
✓ Perpendicular gradient is the negative reciprocal, −1/m.
Quick check
Try these, then reveal the answers.
Gradient of y = 4x − 1?Reveal answer
4
y-intercept of y = −2x + 5?Reveal answer
5
Gradient perpendicular to m = 2?Reveal answer
−1/2
Exam tips
- Rearrange into y = mx + c before reading off m and c.
- Use two clear points to calculate a gradient from a graph.
- For perpendicular lines, take the negative reciprocal of the gradient.
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Frequently asked questions
What do m and c mean?+
m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
How do I find the gradient between two points?+
Divide the difference in y-values by the difference in x-values: (y₂ − y₁)/(x₂ − x₁).
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