Pure · Coordinate geometry
Chapter 1 · 3
The idea
Straight lines
The gradient of a line as a constant rate of change, the three forms of a line's equation — y = mx + c, y − y₁ = m(x − x₁), and ax + by + c = 0 — and how to move between them.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Coordinate geometry
Straight lines
The gradient of a line as a constant rate of change, the three forms of a line's equation — y = mx + c, y − y₁ = m(x − x₁), and ax + by + c = 0 — and how to move between them.
Why it works
One number is the line
A line is straight precisely because its steepness never changes. Pick any two points on it, and , and the gradient comes out the same every time. That single number — change in per unit change in — is the line. Get the order consistent: whichever point's you put first on top, its must go first on the bottom.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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