Understanding Direct and Inverse Proportion
Direct proportion means two quantities move in the same direction - when one goes up, the other goes up at the same rate. Think of it like speed and distance: drive faster, cover more distance.
We write this as y ∝ x or as an equation y = kx, where k is the constant of proportionality. The graph always gives you a straight line passing through the origin.
Inverse proportion works oppositely - as one quantity increases, the other decreases at the same rate. Picture volume and sound quality on your headphones: turn it up too loud, quality goes down. We write this as y ∝ 1/x or y = k/x.
Quick tip: Inverse proportion graphs create curves that never actually touch the axes - they get close but never reach zero!