Solve y-(-2)=3/5(x-(-4))

$$y - ( - 2 ) = \frac { 3 } { 5 } ( x - ( - 4 ) )$$

Solve for x

$$x=\frac{5y-2}{3}$$

Steps for Solving Linear Equation

The opposite of -2 is 2.

$$y+2=\frac{3}{5}\left(x-\left(-4\right)\right)$$

The opposite of -4 is 4.

$$y+2=\frac{3}{5}\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{5} by x+4.

$$y+2=\frac{3}{5}x+\frac{12}{5}$$

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

$$\frac{3}{5}x+\frac{12}{5}=y+2$$

Subtract \frac{12}{5} from both sides.

$$\frac{3}{5}x=y+2-\frac{12}{5}$$

Subtract \frac{12}{5} from 2 to get -\frac{2}{5}.

$$\frac{3}{5}x=y-\frac{2}{5}$$

Divide both sides of the equation by \frac{3}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{5}x}{\frac{3}{5}}=\frac{y-\frac{2}{5}}{\frac{3}{5}}$$

Dividing by \frac{3}{5} undoes the multiplication by \frac{3}{5}.

$$x=\frac{y-\frac{2}{5}}{\frac{3}{5}}$$

Divide y-\frac{2}{5} by \frac{3}{5} by multiplying y-\frac{2}{5} by the reciprocal of \frac{3}{5}.

$$x=\frac{5y-2}{3}$$

Solve for y

$$y=\frac{3x+2}{5}$$

Solution Steps

The opposite of -2 is 2.

$$y+2=\frac{3}{5}\left(x-\left(-4\right)\right)$$

The opposite of -4 is 4.

$$y+2=\frac{3}{5}\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{5} by x+4.

$$y+2=\frac{3}{5}x+\frac{12}{5}$$

Subtract 2 from both sides.

$$y=\frac{3}{5}x+\frac{12}{5}-2$$

Subtract 2 from \frac{12}{5} to get \frac{2}{5}.

$$y=\frac{3}{5}x+\frac{2}{5}$$