Gradient of Linear Graphs

What is Gradient of Linear Graphs?

A single number measuring the steepness and direction of a straight line, equal to the change in y divided by the corresponding change in x between any two points on the line. On the Core route it is read from a grid: draw a gradient triangle between two points where the line crosses grid intersections, count the change in y and the change in x, and divide. On the Extended route it is also calculated from the coordinates of two points as (y2 minus y1) divided by (x2 minus x1), with the same subtraction order used in numerator and denominator. A positive gradient rises from left to right, a negative gradient falls, a horizontal line has gradient zero, and a vertical line has an undefined gradient because its change in x is zero.

This definition is part of the Coordinate Geometry chapter in Cambridge IGCSE Mathematics.

Concepts related to Gradient of Linear Graphs

• rise and run
• gradient triangle
• rate of change
• undefined gradient