For two quantities to have a proportional relationship the graph representing their relationship must be a straight line.
This simply implies that the rate of change in one quantity, when divided by the rate of change in the other one is always the same (constant) at every point on the line, that is for every given set of values.
To illustrate,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{y_3-y_2}{x_3-x_2} \end{gathered}[/tex]The slope for these two points must be the same, and the graph MUST BE A STRAIGHT LINE.
