What is the translation law of the general formula of linear equation in high school mathematics?

The general equation of a straight line can be written as ax+by+c = 0;

The equation is a (x-a)+by+c = 0 after translating one unit to the right along the X axis;

The equation is a (x+a)+by+c = 0 after translating one unit to the right along the X axis;

After translating one unit along the Y axis, the equation is AX+B (Y-A)+C = 0;

After translating one unit along the Y axis, the equation is AX+B (Y+A)+C = 0;

That is, if it is large, it will decrease, and if it is large, it will increase;

On the outside, it is regarded as the case that the X axis and the Y axis respectively translate;

For example, AX+BY+C+D=0 equals A(X+D/A)+BY+C=0 equals AX+B(Y+D/B)+C=0.