Solve the linear equation of a specified point and a specified direction

Given point ：
$$(x_0,y_0)$$
Given direction ：
$$\theta$$
Let the linear equation be ：
$$y=kx+b$$
be ：
$$k=tan\theta$$
$$b=y_0-x_{0}tan\theta$$
Then the linear equation is ：
$$y=tan\theta x+y_0-x_{0}tan\theta$$
in consideration of $\theta =\pm \frac{\pi }{2}$ when , k meaningless , And then it turns into ：
$$cos\theta y=sin\theta x+cos\theta y_0-x_{0}sin\theta$$
Convert to $ax+by+c=0$ The standard form of ：
$$sin\theta x-cos\theta y+cos\theta y_0-x_{0}sin\theta =0$$