How to turn line around point of cross with other line?

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my question seems to be very easy, but I can't figure it out. Maybe someone could help. I know rounding the line around the point $(P_x,P_y)$ is very easy, just like that:

$f(x) = R(x-P_x)+P_y$

Where $R$ is my rounding (slope) parameter.

But what in case if I have my rounded line given by that equation:

$f_1(x) = Rx + T\ \ \ $ - (where $T$ is some moving parameter - up and down).

And I want to turn it round the point of crossing with that line:

$f_2(x)=Ax$

It seems to be obvious that I should find that crossing point, which is very easy, and it is:

$P _ { x } = \frac { T } { ( A - R ) };\ \ \ \ \ P _ { y } = \frac { A T } { ( A - R ) }$

But please notice that my crossing point is dependent on $R$, so every time I change the slope (which is $R$), my crossing point will be changed also.

Do I need separate slope parameter like $R_2$? Or is there any other option?

For any help thanks in advance.