If \(y = mx + b\), what do \(m\) and \(b\) represent?

In the equation (y = mx + b), which represents the slope-intercept form of a linear equation, the variables (m) and (b) have specific meanings related to the graph of the equation.

The variable (m) represents the slope of the line. The slope indicates how steep the line is and the direction it travels as (x) increases. A positive slope means that as (x) increases, (y) also increases; conversely, a negative slope means that as (x) increases, (y) decreases. The slope can also be understood as the "rise over run," which quantifies the vertical change per horizontal change between any two points on the line.

The variable (b) represents the y-intercept of the line. This is the point where the line crosses the y-axis, which occurs when (x = 0). The value of (b) gives the exact point on the y-axis that corresponds to the function’s output when no input variable ((x)) is present.

Thus, the use of slope and y-intercept in this context provides a straightforward understanding of the linear relationship described by the equation, making it easy to