A-level maths / Pure 1 / Straight-line graphs
Straight-line graphs
Connect equations with direction, distance, area and real-world predictions.
Change a point or a model yourself, keep the explanation beside it, then check your understanding with worked practice.
- Gradients and equations of linesFind gradients, line equations and intercepts from points. Use point-gradient form, solve intersections and handle vertical or coincident points correctly.
- Parallel and perpendicular linesFind equations of parallel and perpendicular lines, explain the negative-reciprocal rule and prove geometric properties using exact gradients.
- Distance and area in coordinate geometryCalculate exact distances, shortest perpendicular distances and triangle or quadrilateral areas. Combine line intersections with geometry and explore triangle altitudes.
- Linear modellingBuild straight-line models from data, interpret gradient and intercept with units, assess fit and distinguish interpolation, extrapolation and direct proportion.
Useful foundations
Review simultaneous equations for intersections, or surds for exact lengths.