In a linear equation represented as y = mx + b, what does the 'm' represent?

In the linear equation represented by ( y = mx + b ), the 'm' specifically indicates the slope of the line. The slope is a measure of how steep the line is and represents the rate of change of ( y ) with respect to ( x ). This means that for every unit increase in ( x ), ( y ) changes by an amount equal to 'm'. A positive slope indicates that as ( x ) increases, ( y ) also increases, while a negative slope shows that as ( x ) increases, ( y ) decreases.

Understanding the role of the slope is essential as it helps in determining the direction of the line on the Cartesian plane. The slope can also be interpreted as the rise over run — the vertical change divided by the horizontal change between any two points on the line. This foundational concept is crucial for analyzing linear relationships in various mathematical contexts.