Solve y-2=-sqrt{3}(x+1)

$$y-2=- \sqrt{ 3 } (x+1)$$

Solve for x

$$x=-\frac{\sqrt{3}\left(y+\sqrt{3}-2\right)}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\sqrt{3} by x+1.

$$y-2=\left(-\sqrt{3}\right)x-\sqrt{3}$$

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

$$\left(-\sqrt{3}\right)x-\sqrt{3}=y-2$$

Add \sqrt{3} to both sides.

$$\left(-\sqrt{3}\right)x=y-2+\sqrt{3}$$

Reorder the terms.

$$-\sqrt{3}x=y+\sqrt{3}-2$$

The equation is in standard form.

$$\left(-\sqrt{3}\right)x=y+\sqrt{3}-2$$

Divide both sides by -\sqrt{3}.

$$\frac{\left(-\sqrt{3}\right)x}{-\sqrt{3}}=\frac{y+\sqrt{3}-2}{-\sqrt{3}}$$

Dividing by -\sqrt{3} undoes the multiplication by -\sqrt{3}.

$$x=\frac{y+\sqrt{3}-2}{-\sqrt{3}}$$

Divide y+\sqrt{3}-2 by -\sqrt{3}.

$$x=-\frac{\sqrt{3}\left(y+\sqrt{3}-2\right)}{3}$$

Solve for y

$$y=-\sqrt{3}\left(x+1\right)+2$$