A straight line can be completely described by its slope together with a single point…

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

A straight line can be completely described by its slope together with a single point lying on it. (i) Define the slope of a line passing through two distinct points

(x_1,y_1)

and

(x_2,y_2)

where

x_1\neq x_2

. (ii) Give a logical argument to show that, in the Cartesian plane, specifying one point and a slope determines one and only one straight line.

Related theory

Straight Lines
Coordinate Geometry
Slope and angle between lines
Functions
Slope using coordinates

Browse the problem library