Which formula represents the slope of a line?

The formula that represents the slope of a line is given by the change in the vertical coordinate (y-values) over the change in the horizontal coordinate (x-values) between two distinct points on that line. Specifically, this is expressed as (y2 - y1) / (x2 - x1). This formula calculates how steep the line is by measuring the rise (the difference in y-values) over the run (the difference in x-values).

When you apply this formula, you can determine whether the line is increasing or decreasing, and the value of the slope can indicate the rate of change. A positive slope means the line rises as it moves from left to right, while a negative slope indicates a decrease. A slope of zero indicates a horizontal line, and an undefined slope occurs with vertical lines.

The other options represent different mathematical expressions. The first option, y = mx + b, is the equation of a line in slope-intercept form, where 'm' is the slope, but it does not directly calculate the slope itself. The second option, y = x² + bx + c, represents a quadratic function, not a linear one. The last option, y² = a + b, does not denote a linear