Solve y=x+atanp

$$y = x + a \tan p$$

Solve for a

$$\left\{\begin{matrix}a=\left(y-x\right)\cot(p)\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\left(p>\frac{\pi n_{3}}{2}\text{ and }p<\frac{\pi n_{3}}{2}+\frac{\pi }{2}\right)\\a\in \mathrm{R}\text{, }&y=x\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }p=\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }p=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x+a\tan(p)=y$$

Subtract x from both sides.

$$a\tan(p)=y-x$$

The equation is in standard form.

$$\tan(p)a=y-x$$

Divide both sides by \tan(p).

$$\frac{\tan(p)a}{\tan(p)}=\frac{y-x}{\tan(p)}$$

Dividing by \tan(p) undoes the multiplication by \tan(p).

$$a=\frac{y-x}{\tan(p)}$$

Divide y-x by \tan(p).

$$a=\left(y-x\right)\cot(p)$$