Conquer the College Math Placement Challenge 2025 – Step Up and Shine!

The slope (m) in the equation y = mx + b represents the rate of change of the dependent variable (y) with respect to the independent variable (x). Specifically, it tells us how much y changes for a unit change in x. The phrase "rise over run" is a common way to define the slope, where "rise" refers to the vertical change (the change in y) and "run" refers to the horizontal change (the change in x). This can be expressed mathematically as:

\[ m = \frac{\Delta y}{\Delta x} \]

In practical terms, if you were to plot two points on the line described by the equation, you could calculate the slope by measuring how far up (rise) you move for each unit you move to the right (run).

This understanding is fundamental in analyzing linear relationships, as the slope indicates not only direction (positive or negative) but also the steepness of the line. Thus, recognizing the slope as "rise over run" establishes a clear connection between the graphical representation of linear equations and their algebraic forms.