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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

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

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

Add \frac{4}{3} to both sides.

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

Add -4 and \frac{4}{3} to get -\frac{8}{3}.

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

Divide both sides of the equation by -\frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by -\frac{2}{3} undoes the multiplication by -\frac{2}{3}.

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

Divide y-\frac{8}{3} by -\frac{2}{3} by multiplying y-\frac{8}{3} by the reciprocal of -\frac{2}{3}.

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

Solve for y

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

Solution Steps

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

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

Add 4 to both sides.

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

Add -\frac{4}{3} and 4 to get \frac{8}{3}.

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