Switch between direct proportion (y=kx) and inverse proportion (y=k/x) with the tabs, and adjust k with the slider. Compare just how differently the two graphs are shaped.
In both direct and inverse proportion, two quantities affect each other — but in exactly opposite directions.
If one piece of candy costs 500 won, two cost 1000 won, and three cost 1500 won. As the quantity (x) increases, the price (y) increases by exactly the same ratio — that's direct proportion. Graphed, it's a straight line through the origin.
Now say you're driving a 60km distance. At 60km/h it takes 1 hour; at 120km/h (twice as fast), it takes 30 minutes (half as long). As the speed (x) increases, the time (y) actually decreases — that's inverse proportion. Instead of a straight line, the graph is a smooth curve that gets closer and closer to the x-axis and y-axis without ever touching them.
Both share something in common: for direct proportion, y÷x always stays the same value (k); for inverse proportion, x×y always stays the same value (k). Switch between the tabs and compare how differently the numbers in the table move for each.