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

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-4.

$$y-4=\frac{2}{3}x-\frac{8}{3}$$

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

$$\frac{2}{3}x-\frac{8}{3}=y-4$$

Add \frac{8}{3} to both sides.

$$\frac{2}{3}x=y-4+\frac{8}{3}$$

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

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

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

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

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

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

Divide y-\frac{4}{3} by \frac{2}{3} by multiplying y-\frac{4}{3} by the reciprocal of \frac{2}{3}.

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

Solve for y

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

Solution Steps

Use the distributive property to multiply \frac{2}{3} by x-4.

$$y-4=\frac{2}{3}x-\frac{8}{3}$$

Add 4 to both sides.

$$y=\frac{2}{3}x-\frac{8}{3}+4$$

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

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