Chapter 2 Linear Equations and Functions - 2.5 Model Direct Variations - 2.5 Exercises - Skill Practice - Page 110: 37

See below.

If the variables vary directly, then $y=ax$ for some constant $a$. Plugging in the given values, here $y_1=ax_1\\a=\frac{y_1}{x_1}$ and $y_2=ax_2\\a=\frac{y_2}{x_2}$ Thus $a=\frac{y_1}{x_1}=\frac{y_2}{x_2}\\\frac{x_2}{x_1}=\frac{y_2}{y_1}$. Thus we proved what we had to.