Generally speaking, in a plane rectangular coordinate system, if a straight line L passes through points A(X1,Y1) and B(X2,Y2), where x1≠x2, then AB=(x2-x1,y2-y1) is a direction vector of L, so the slope of the straight line L is k=(y2-y1)/(x2-x1), and from k=tanα (0≤α<π), the inclination angle α of the straight line L can be calculated. Let tanα=k, and the equation y-y0=k(x-x0) is called the point-slope form of the straight line, where (x0,y0) is a point on the straight line.

When α is π/2 (90 degrees, the straight line is perpendicular to the X-axis), tanα is meaningless and there is no point-slope equation.

Point-slope equations are commonly used in derivatives. They are used to find the equation of a tangent line using the derivative of a point on the tangent line and the equation of the curve (the slope of the tangent line at a point on the equation). They are suitable for problems where you need to find the equation of a line when you know the coordinates of a point and the slope of the line.