Page "Analytic geometry" Paragraph 11

In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation.

For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.

These points form a line, and y = x is said to be the equation for this line.

In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures.