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This lesson covers Coordinate Geometry as required by the A-Level Mathematics Pure 1 specification. Coordinate geometry connects algebra with geometry by using equations to describe lines, curves, and circles on a Cartesian plane. This topic is fundamental and appears throughout the A-Level course.
The gradient of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ − y₁) / (x₂ − x₁)
| Form | Equation | Use |
|---|---|---|
| Gradient-intercept | y = mx + c | When gradient and y-intercept are known |
| Point-gradient | y − y₁ = m(x − x₁) | When gradient and a point are known |
| General form | ax + by + c = 0 | Standard form for answers |
Example: Find the equation of the line through (2, 5) with gradient 3.
y − 5 = 3(x − 2)
y − 5 = 3x − 6
y = 3x − 1
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