What is the Directly Proportional Symbol? ($\propto$)

The symbol for 'is proportional to' is: $\propto$.

• It looks like an infinity symbol ($\infty$) with the right side chopped off, or similar to the Greek lowercase letter alpha ($\alpha$).
• Example: If we write $y \propto x$, we read it aloud as: "$y$ is directly proportional to $x$."

When two variables are directly proportional, it means they increase or decrease together at the exact same rate.

• If $x$ doubles, $y$ also doubles.
• If $x$ is cut in half, $y$ is also cut in half.
• Real-Life Example: The total cost (C) of buying apples is directly proportional to the number (N) of apples you buy. ($C \propto N$).

You cannot solve an algebra problem using a $\propto$ sign. You must convert it into an 'equals' ($=$) sign to do math.

• To do this, you replace the $\propto$ symbol with an $=$ sign, but you MUST introduce a constant multiplier, usually represented by the letter k.
• So, $y \propto x$ mathematically becomes: $y = kx$.
• (Here, 'k' is called the Constant of Proportionality).

If two things are inversely proportional (when one increases, the other decreases), we still use the same symbol, but we put the second variable under the number 1 (as a fraction).

• Written as: $y \propto \frac{1}{x}$