Final answer:
The slope of a line indicates the line's steepness and direction on a graph, with positive slope meaning an upward trend as x increases and negative slope meaning a downward trend.
Step-by-step explanation:
The slope of a line in a graph represents how steep the line is and the direction it moves across the coordinate plane. In a linear equation of the form y = mx + b, the slope is represented by the variable m, and is calculated as the rise over the run, meaning the change in y over the change in x. A positive slope signifies that the line ascends as the x-values increase, while a negative slope indicates that the line descends. The slope is consistent throughout any part of a straight line. For instance, if the y-intercept is 9 and the slope is 3, this means for every unit you move to the right along the x-axis, the line rises 3 units on the y-axis. This steepness and direction are important characteristics of a line's equation and can tell us a great deal about the nature of the relationship it represents.