Rise Over Run 591083
1. Let's clarify the concept of "rise over run."
2. "Rise over run" is a way to describe the slope of a line in coordinate geometry.
3. The slope $m$ of a line is calculated as the change in $y$ (vertical change, or "rise") divided by the change in $x$ (horizontal change, or "run").
4. Mathematically, this is written as $$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
5. If you have an equation with $x$ in it, such as $y = mx + b$, the coefficient $m$ in front of $x$ represents the slope, which is the "rise over run."
6. So yes, the value multiplied by $x$ in a linear equation is considered the "rise over run," or slope, indicating how much $y$ changes for a unit change in $x$.