The definition you're describing is known as slope.
In mathematical terms, the slope of a line is calculated as the "rise" over the "run," where:
- Rise refers to the change in the y-coordinate (vertical change) between two points on the line.
- Run refers to the change in the x-coordinate (horizontal change) between the same two points.
Mathematically, the slope \( m \) can be expressed as:
\[ m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
- A positive slope indicates that the line rises as it moves from left to right.
- A negative slope indicates that the line falls as it moves from left to right.
- A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.
The concept of slope is fundamental in algebra and calculus, as it reveals information about the rate of change of a function or relationship between variables.