In the slope-intercept form of a linear equation, what does 'm' represent?

In the slope-intercept form of a linear equation, which is expressed as ( y = mx + b ), the symbol 'm' specifically represents the slope of the line. The slope indicates how steep the line is and the direction in which it moves.

More concretely, the slope is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. This means that if you move one unit horizontally (along the x-axis), the slope tells you how many units you will move vertically (along the y-axis). A positive slope indicates that the line rises as it moves from left to right, while a negative slope indicates that the line falls.

Identifying 'm' correctly is crucial in graphing linear equations and understanding the relationship between the variables represented in the equation. This knowledge aids in predicting the behavior of the line as well as in solving real-world problems related to linear relationships.