When does a ratio table show proportionality?

A proportional relationship keeps the same ratio between two quantities. In the illustration, each fictional kit supplies three markers and there are no extra markers outside the kits. One kit gives three markers, two give six, and three give nine.

For every nonzero kit count, dividing the marker count by the kit count gives three markers per kit. This constant ratio is called the unit rate. Writing the kit count as x and marker count as y gives the rule y = 3x. With no kits, there are no markers, so the rule also includes the point (0,0), called the origin.

The plotted values lie on a straight line through that origin. Both features matter. If two markers are already present before any kits arrive, the rule becomes y = 3x + 2. Each extra kit still adds three, so the graph is straight, but it starts at two rather than zero.

That extra starting amount makes the ratios vary: one kit corresponds to five markers and two kits to eight. A constant increase is therefore not enough to establish proportionality. The whole relationship must preserve the constant ratio, with the zero-input point consistent with the rule; the ratio y/x itself is not calculated at zero.