Solve y-8/3=1/3(x-2)

$$y - \frac { 8 } { 3 } = \frac { 1 } { 3 } ( x - 2 )$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-2.

$$y-\frac{8}{3}=\frac{1}{3}x-\frac{2}{3}$$

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

$$\frac{1}{3}x-\frac{2}{3}=y-\frac{8}{3}$$

Add \frac{2}{3} to both sides.

$$\frac{1}{3}x=y-\frac{8}{3}+\frac{2}{3}$$

Add -\frac{8}{3} and \frac{2}{3} to get -2.

$$\frac{1}{3}x=y-2$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{y-2}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$x=\frac{y-2}{\frac{1}{3}}$$

Divide y-2 by \frac{1}{3} by multiplying y-2 by the reciprocal of \frac{1}{3}.

$$x=3y-6$$

Solve for y

$$y=\frac{x+6}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by x-2.

$$y-\frac{8}{3}=\frac{1}{3}x-\frac{2}{3}$$

Add \frac{8}{3} to both sides.

$$y=\frac{1}{3}x-\frac{2}{3}+\frac{8}{3}$$

Add -\frac{2}{3} and \frac{8}{3} to get 2.

$$y=\frac{1}{3}x+2$$