Solve xcosθ+ysinθ+1=0

$$x \cos \theta + y \sin \theta + 1 = 0$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{x\cos(\theta )+1}{\sin(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\\y\in \mathrm{R}\text{, }&x=-\frac{1}{\cos(\theta )}\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x\cos(\theta ) from both sides. Anything subtracted from zero gives its negation.

$$y\sin(\theta )+1=-x\cos(\theta )$$

Subtract 1 from both sides.

$$y\sin(\theta )=-x\cos(\theta )-1$$

The equation is in standard form.

$$\sin(\theta )y=-x\cos(\theta )-1$$

Divide both sides by \sin(\theta ).

$$\frac{\sin(\theta )y}{\sin(\theta )}=-\frac{x\cos(\theta )+1}{\sin(\theta )}$$

Dividing by \sin(\theta ) undoes the multiplication by \sin(\theta ).

$$y=-\frac{x\cos(\theta )+1}{\sin(\theta )}$$