What does the Two Point Formula represent?

The Two Point Formula, represented as ( y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) ), is used to determine the equation of a line when you have two distinct points on that line, labeled as ((x_1, y_1)) and ((x_2, y_2)).

This formula calculates the slope of the line, which is given by (\frac{y_2 - y_1}{x_2 - x_1}). The slope is then used to express the linear relationship between (y) and (x), starting from one of the points, hence the term (y - y_1) shows how the change in (y) depends on the change in (x).

The utility of the Two Point Formula lies in its straightforward approach to finding the equation of a line without needing to rearrange it into other forms first. This is especially helpful in coordinate geometry, where direct application of the coordinates can quickly yield the line's equation.

The other forms listed—such as the slope-intercept form (y = mx + b), the standard