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

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

Solve for x

$$x=\frac{13-3y}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Subtract \frac{4}{3} from both sides.

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

Subtract \frac{4}{3} from -3 to get -\frac{13}{3}.

$$-\frac{2}{3}x=y-\frac{13}{3}$$

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

$$\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{y-\frac{13}{3}}{-\frac{2}{3}}$$

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

$$x=\frac{y-\frac{13}{3}}{-\frac{2}{3}}$$

Divide y-\frac{13}{3} by -\frac{2}{3} by multiplying y-\frac{13}{3} by the reciprocal of -\frac{2}{3}.

$$x=\frac{13-3y}{2}$$

Solve for y

$$y=\frac{13-2x}{3}$$

Solution Steps

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

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

Add 3 to both sides.

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

Add \frac{4}{3} and 3 to get \frac{13}{3}.

$$y=-\frac{2}{3}x+\frac{13}{3}$$