How to Determine Whether Two Variables Are Directly Proportional

Step-by-Step Guide

1. 1

   Step 1: Understand direct proportion.

   Two variables are in direct proportion if each variable changes at the same rate.In other words, if x{\displaystyle x} changes by a certain factor or constant (k{\displaystyle k}), then y{\displaystyle y} changes by that same constant (k{\displaystyle k}). , The equation will have two variables and a constant.
   
   If you are not given the equation, you cannot use this method.
   
   For example, you might be given the equation yx=32{\displaystyle {\frac {y}{x}}={\frac {3}{2}}}. , The equation is y=kx{\displaystyle y=kx}, where y{\displaystyle y} equals the y-coordinate of a point on the line, x{\displaystyle x} equals the x-coordinate for that same point, and k{\displaystyle k} is the constant, or slope of the line.
   
   Use algebra to rearrange the equation in the form of y=kx{\displaystyle y=kx}.
   
   If you can’t rewrite the equation in this form, the variables are not directly proportional.
   
   If you can, it proves that they are directly proportional.For example, if you multiply both sides of the equation yx=32{\displaystyle {\frac {y}{x}}={\frac {3}{2}}} by x{\displaystyle x}, the equation becomes y=32x{\displaystyle y={\frac {3}{2}}x}, which is in the form of y=kx{\displaystyle y=kx}, with 32{\displaystyle {\frac {3}{2}}} being the constant.
2. 2

   Step 2: Write down the equation of the line.

3. 3

   Step 3: Rewrite the equation in the form of direct proportion

4. 4

   Step 4: or variation.

Detailed Guide

About the Author