What does the slope of a line measure?

The slope of a line measures the steepness of that line. Mathematically, it is defined as the change in the vertical direction (rise) divided by the change in the horizontal direction (run) between any two points on the line. This ratio indicates how much the line rises or falls as you move from left to right. A larger absolute value of the slope corresponds to a steeper line, while a slope of zero indicates a horizontal line.

Understanding slope is fundamental in various contexts, such as analyzing linear functions in mathematics, interpreting graphical data, and even understanding rates of change in real-world scenarios. The concept of steepness helps in visualizing how quickly or slowly a variable changes relative to another, which can have practical applications in fields like physics, economics, and engineering.