Which formula represents the slope of a line?

The formula that represents the slope of a line is derived from the change in the vertical direction (rise) over the change in the horizontal direction (run) between two points on the line. The correct formula, which is (y₂ - y₁) / (x₂ - x₁), captures this relationship accurately.

Here, y₂ and y₁ represent the y-coordinates of two distinct points on the line, while x₂ and x₁ represent their corresponding x-coordinates. The numerator (y₂ - y₁) indicates how much the y-value changes as you move from one point to the other, and the denominator (x₂ - x₁) shows how much the x-value changes in the same interval.

This ratio effectively gives the steepness or angle of the line with respect to the horizontal axis. A positive slope indicates that the line rises as it moves from left to right, while a negative slope shows that it falls. If the slope is zero, it indicates a horizontal line, and if it is undefined (as is the case when the x-coordinates are equal), it signifies a vertical line.

The other options do not define the slope. For instance, the second option revers