Edexcel International GCSE Mathematics A · 4MA1
Straight-line graphs
The equation y = mx + c describes a straight line with gradient m and vertical intercept c. Two points determine its gradient when their x-coordinates differ. A vertical line has equation x = constant and no finite gradient.
Key method
Calculate m = (y₂ − y₁)/(x₂ − x₁), then substitute a point to find c. Use coordinates in the same subtraction order in numerator and denominator.
Worked example
Find the line through (2, 5) and (6, 13).
- The gradient is (13 − 5)/(6 − 2) = 8/4 = 2.
- Substitute (2, 5) into y = 2x + c: 5 = 4 + c.
- Thus c = 1. Check the second point: 2(6) + 1 = 13.
Answer and interpretation
y = 2x + 1.
Common mistake
Using the first point’s y-coordinate as c ignores that the intercept occurs where x = 0.
Practise independently
Find the gradient of a line perpendicular to y = 2x + 1.
Check your answer
−1/2, since the gradients of perpendicular non-vertical lines multiply to −1.
Syllabus connection
This lesson develops equation of a straight line within the graphs and coordinate geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
Content updated: .