Graphs of direct proportion and inverse proportion
Plot a direct proportion from a table, find k from one point, fit y = k/x to a point with a slider, spot the direct-proportion graph and plot an inverse proportion.
- UK: Year 9
- France: grade 7
- Germany: grade 6
- Syria: grade 8
- Ukraine: grade 8
- Russia: grade 8
Guide
Two quantities are in direct proportion when y = kx: double x and y doubles too. The graph is a straight line through the origin (0, 0). k is the gradient: how much y grows for each 1 of x. Find it from any point on the line: k = y ÷ x.
Careful: not every straight line is direct proportion. The line y = x + 3 is straight, but it does not go through (0, 0), so doubling x does not double y. A falling straight line is not proportion either.
Two quantities are in inverse proportion when y = k/x, so x × y = k stays the same: double the workers and the job takes half the days. The graph is a curve that falls steeply, then levels out. It never touches either axis: x × y can never be k if x or y is 0.