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

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

Solve for x

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

Steps for Solving Linear Equation

The opposite of -2 is 2.

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

The opposite of -2 is 2.

$$y+2=\frac{2}{3}\left(x+2\right)$$

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

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

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

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

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

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

Subtract \frac{4}{3} from 2 to get \frac{2}{3}.

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

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

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

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

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

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

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

Solve for y

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

Solution Steps

The opposite of -2 is 2.

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

The opposite of -2 is 2.

$$y+2=\frac{2}{3}\left(x+2\right)$$

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

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

Subtract 2 from both sides.

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

Subtract 2 from \frac{4}{3} to get -\frac{2}{3}.

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