To draw a function we first need a place to draw it. That place is the coordinate plane: a flat grid built from two number lines that cross at right angles.

• The horizontal line is the x-axis.
• The vertical line is the y-axis.

They meet at the origin, the point (0, 0). To the right and up the numbers are positive; to the left and down they are negative.

Every point has an address

A point is pinned down by an ordered pair (x, y). The order matters — that is why it is called ordered:

• the first number, x, is how far right (or left, if negative) you go;
• the second number, y, is how far up (or down, if negative) you go.

So to plot (3, 2) you start at the origin, walk 3 right, then 2 up. Note that (3, 2) and (2, 3) are different points. Drag the sliders and watch the address move.

The four quadrants

The two axes slice the plane into four regions called quadrants, numbered with Roman numerals starting from the top-right and going counter-clockwise. The sign of x and y tells you which one a point lives in:

The shaded diagram below labels each quadrant with its sign pattern.

See it in action

Khan Academy gives a friendly tour of the coordinate plane here: