To express relationships between quantities using letters, we utilize variables to represent these quantities and establish their connections through equations.

In mathematics, relationships among various quantities are often denoted by variables, which are typically represented by letters such as $x$, $y$, or $z$. These variables serve as placeholders for numbers, enabling us to formulate general rules or equations. For instance, if we consider a relationship where the total cost $C$ is determined by the number of items $n$ multiplied by the price per item $p$, this can be expressed mathematically as:

Using letters to symbolize relationships simplifies complex problems and facilitates the manipulation and solving of equations. For example, in physics, the relationship among distance $d$, speed $s$, and time $t$ is often represented by the equation:

This equation indicates that distance is the product of speed and time.

In algebra, you will frequently encounter linear relationships, which can be represented in the standard form:

In this equation, $y$ and $x$ are variables, $m$ denotes the slope of the line, and $c$ signifies the y-intercept. This formula illustrates how a straight line is depicted on a graph and elucidates the impact of changes in $x$ on the value of $y$.

By employing letters to represent quantities, we can generalize mathematical concepts and apply them across a diverse array of problems. This approach proves to be a powerful tool in both pure and applied mathematics.