What is the slope of a line in a graph?

The slope of a line in a graph quantitatively represents the steepness or inclination of that line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. A higher slope indicates a steeper line, while a slope close to zero indicates a flatter line. The concept of slope is foundational in understanding linear relationships in mathematics, as it reflects how much the value of one variable changes in relation to another.

For example, a slope of 2 means that for every unit increase in the horizontal direction, the line rises by 2 units. This characteristic helps in visualizing and interpreting the behavior of linear equations and their graphs, aiding in various applications across different contexts in mathematics and real-world situations. Thus, identifying the steepness of the line as its slope provides crucial information about the relationship represented by that line.