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This topic covers the equation of a straight line — y = mx + c and y − y₁ = m(x − x₁) — along with gradients and the conditions for lines to be parallel or perpendicular. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Use y minus y1 equals m times x minus x1 with a point and a gradient. Find the gradient from two points as the change in y over the change in x. Parallel lines share a gradient; perpendicular gradients multiply to minus 1.
Before you start
Start once you are confident with gradients and coordinates. It leads on to perpendicular lines, circles and tangents. Pure 1 is where it is assessed.
What you learn
Everything about a straight line follows from its gradient. From it you get the line's equation, whether two lines are parallel or perpendicular, where they cross, and the area they enclose. Two lines cross where their equations are both true — so solve them simultaneously. The perpendicular bisector of AB is the line that cuts AB in half, at right angles. If a side lies along the x -axis, the height is simply the y -coordinate of the opposite vertex. The course works through gradient and the equation of a line, parallel and perpendicular, where lines meet, the perpendicular bisector and areas and problem solving. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Straight Lines is a Coordinate Geometry topic in the A-level syllabus, covered here at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Students often pair it with Circles — Equation & Properties, Circles — Tangents & Chords, Distance & Midpoint and Parametric Equations. Endless extra practice on this strand is available on the Coordinate Geometry revision engine, which generates a fresh question each time.
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