Section 4.3: Graphing Proportional Relationships

Property

Two variables are proportional if their ratio is always the same. If two variables are proportional, they are related by the equation

where $k$ is the constant of proportionality.

Property

The variables $y$ and $x$ are proportional if

Examples

• The cost $C$ for gallons $g$ of gas is proportional. If 5 gallons cost 20 dollars, the constant is $k = \frac{20}{5} = 4$. The equation is $C = 4g$.
• The number of words $w$ you type is proportional to the minutes $m$ you spend typing. If you type 240 words in 4 minutes, the constant is $k = \frac{240}{4} = 60$. The equation is $w = 60m$.
• The length in centimeters $c$ is proportional to the length in inches $i$. Since 1 inch is 2.54 cm, the constant of proportionality is $k = 2.54$. The equation is $c = 2.54i$.

Explanation

Proportional variables have a constant ratio. This means one variable is always a fixed multiple of the other. Think of it like a recipe: doubling the ingredients doubles the serving size. Their graph is a straight line through the origin (0,0).