How can you use rates to determine wheather a situation is a proportional relationship

If the rate is a constant, the relationship is proportional. (The rate is the constant of porportionality.)

For two or more points on the function curve, divide the dependent variable value by the independent one. If you get the same result in every case, the relationship is porportional.

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Note

For some non-proportional relationships, it is possible to find points on the graph that will pass the above test. If you suspect the relationship is actually not one of proportionality, try more points. Check also to make sure that (0, 0) is on the curve.