Linear Equations: Slope-Intercept Form

A linear equation can be written in multiple forms. One of the most commonly used forms is the slope-intercept form:

where:
- $a$ is the slope (also called the gradient), which describes the direction and steepness of the line.
- $b$ is the y-intercept, representing the y-coordinate of the point where the line crosses the y-axis, located at $(0, b)$.

Note: We will cover the slope in detail in the next topic.

Function Notation:
Once we isolate $y$ in a linear equation (writing it as $y = ax + b$), we can express $y$ in function notation as $y = f(x)$.

In our case, the linear equation $y = ax + b$ becomes:

Using function notation is very useful. For example, it allows us to evaluate the function for specific values of $x$. To find the y-value when $x = 0$, we substitute $0$ for $x$:

This shows that when $x = 0$, the function value is $b$, which corresponds directly to the y-intercept at the point $(0, b)$.