HSC · Topic explainer
How do Cartesian coordinates work?
The Cartesian plane uses two perpendicular number lines. In an ordered pair (x, y), x gives the horizontal position and y gives the vertical position. The axes meet at (0, 0). At the intersection of two graphs, the same pair satisfies both equations, so solve for one coordinate and substitute to find the other.
Worked example
Find where y = 2x + 1 and y = 5 − 2x meet. Both expressions equal y at the intersection, so 2x + 1 = 5 − 2x. Then 4x = 4 and x = 1.
Substitute x = 1 into either line to get y = 3. Plot the point (1, 3) one unit right and three units up. Substitution into both original equations confirms that both lines pass through this point.
Official exam practice
Find other years and marking guidance in the Mathematics Advanced official exam archive.