Solve y-4=1/3(x-2)

$$y-4= \frac{ 1 }{ 3 } (x-2)$$

Solve for x

$$x=3y-10$$

Steps for Solving Linear Equation

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

$$y-4=\frac{1}{3}x-\frac{2}{3}$$

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

$$\frac{1}{3}x-\frac{2}{3}=y-4$$

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

$$\frac{1}{3}x=y-4+\frac{2}{3}$$

Add -4 and \frac{2}{3} to get -\frac{10}{3}.

$$\frac{1}{3}x=y-\frac{10}{3}$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{y-\frac{10}{3}}{\frac{1}{3}}$$

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

$$x=\frac{y-\frac{10}{3}}{\frac{1}{3}}$$

Divide y-\frac{10}{3} by \frac{1}{3} by multiplying y-\frac{10}{3} by the reciprocal of \frac{1}{3}.

$$x=3y-10$$

Solve for y

$$y=\frac{x+10}{3}$$

Solution Steps

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

$$y-4=\frac{1}{3}x-\frac{2}{3}$$

Add 4 to both sides.

$$y=\frac{1}{3}x-\frac{2}{3}+4$$

Add -\frac{2}{3} and 4 to get \frac{10}{3}.

$$y=\frac{1}{3}x+\frac{10}{3}$$