Solve y=-frac{sqrt{3}}{3}x+3

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

Solve for x

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

Steps for Solving Linear Equation

Express \left(-\frac{\sqrt{3}}{3}\right)x as a single fraction.

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

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

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

Subtract 3 from both sides.

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

Multiply both sides of the equation by 3.

$$-\sqrt{3}x=3y-9$$

The equation is in standard form.

$$\left(-\sqrt{3}\right)x=3y-9$$

Divide both sides by -\sqrt{3}.

$$\frac{\left(-\sqrt{3}\right)x}{-\sqrt{3}}=\frac{3y-9}{-\sqrt{3}}$$

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

$$x=\frac{3y-9}{-\sqrt{3}}$$

Divide -9+3y by -\sqrt{3}.

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

Solve for y

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