What is the point-slope form of a linear equation?

The point-slope form of a linear equation is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a specific point on the line, and m is the slope of the line. This format is particularly useful because it allows you to quickly write the equation of a line when you know a single point it passes through and the slope.

The structure of the point-slope form makes it evident how the line behaves with respect to that specific point. By manipulating this equation, you can easily derive the slope or the coordinates of any point along the line. This form is foundational for understanding linear relationships and transitions into other forms of linear equations, such as slope-intercept and standard forms.

In contrast, the other forms listed do not represent the point-slope format. The slope-intercept form (y = mx + b) focuses on the y-intercept rather than a specific point and slope. The equation Ax + By = C represents standard form but lacks the clarity about slope and specific points. The equation y = k/x denotes a nonlinear relationship, often associated with inverse variations, which does not relate to linear equations at all. Thus, the point-slope form stands out