Coordinates

The coordinate plane uses two perpendicular number lines (axes) to locate any point using an ordered pair (x, y). It is divided into four quadrants.

The gradient (slope) of a line measures how steep it is — how much the line rises or falls for every unit it moves to the right. Gradient = change in y ÷ change in x (rise ÷ run).

The midpoint of a line segment is the point exactly halfway between its endpoints. The distance formula uses Pythagoras' theorem to find the straight-line distance between any two points on a coordinate grid.

Every straight-line graph can be written as y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). Knowing these two values is enough to draw or describe any straight line.