The Slope-Intercept Form

In real-life scenarios, the **y-intercept ($b$) is often called the initial value**. It is the 'starting line' before any action happens. If you are tracking the height of a plant that is already 5 inches tall when you buy it, $b = 5$. The **slope ($m$) is the rate of change**—how much the $y$ value changes for every single unit of $x$. If that plant grows 2 inches per week, $m = 2$. Putting it together, your growth equation is $y = 2x + 5$.

Sometimes you know the slope ($m$), but you don't know the starting point ($b$). Instead, you just have one point $(x, y)$ that the line passes through. To find $b$, you simply plug the $x$, $y$, and $m$ values into the formula $y = mx + b$ and solve for the missing piece. This is like having a map and one coordinate; you can use the 'steepness' to backtrack and find exactly where the path began on the $y$-axis.