In the point-slope form of a line, what is the correct equation?

The point-slope form of a line is represented by the equation that expresses the relationship between the slope of the line and a specific point that the line passes through. This form is particularly useful because it allows one to easily sketch the line when given a point on the line and the slope.

In the correct equation, ( y - y₁ = m(x - x₁) ), ( m ) represents the slope of the line, and ( (x₁, y₁) ) is a point on that line. This formulation shows how any point ( (x, y) ) that lies on the line can be generated from the known point ( (x₁, y₁) ) by utilizing the slope ( m ). The equation is structured such that it indicates the vertical change (( y - y₁ )) is directly proportional to the horizontal change (( x - x₁ )) through the slope ( m ).

This form is particularly advantageous in both algebra and geometry, as it can be used to easily solve for ( y ) and convert to other forms of linear equations, such as the slope-intercept form ( y = mx + b ), but specifically incorporates