Which equation represents the point-slope form of a linear equation?

The point-slope form of a linear equation is represented by the equation where ( y - y_1 = m(x - x_1) ). In this format, ( m ) represents the slope of the line, while ( (x_1, y_1) ) is a specific point on the line. This form is particularly useful because it allows you to quickly write the equation of a line when you know the slope and a point through which the line passes.

This form emphasizes the relationship between any point on the line and the known point ( (x_1, y_1) ), capturing how much ( y ) varies from ( y_1 ) in relation to how much ( x ) varies from ( x_1 ). As such, it directly highlights the slope's role in determining the steepness and direction of the line.

The other equations listed represent different forms of linear equations, but they do not fit the definition of point-slope form. For instance, one of the options is the slope-intercept form ( y = mx + b ), where ( b ) represents the y-intercept rather than a specific point on the line, and another depicts the standard form with