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

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

Solve for x

$$x=10-3y$$

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}.

$$x=10-3y$$

Solve for y

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

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}.

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