Solve (y-3)=-4/5(x+7)

$$( y - 3 ) = - \frac { 4 } { 5 } ( x + 7 )$$

Solve for x

$$x=\frac{-5y-13}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{4}{5} by x+7.

$$y-3=-\frac{4}{5}x-\frac{28}{5}$$

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

$$-\frac{4}{5}x-\frac{28}{5}=y-3$$

Add \frac{28}{5} to both sides.

$$-\frac{4}{5}x=y-3+\frac{28}{5}$$

Add -3 and \frac{28}{5} to get \frac{13}{5}.

$$-\frac{4}{5}x=y+\frac{13}{5}$$

Divide both sides of the equation by -\frac{4}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{4}{5}x}{-\frac{4}{5}}=\frac{y+\frac{13}{5}}{-\frac{4}{5}}$$

Dividing by -\frac{4}{5} undoes the multiplication by -\frac{4}{5}.

$$x=\frac{y+\frac{13}{5}}{-\frac{4}{5}}$$

Divide y+\frac{13}{5} by -\frac{4}{5} by multiplying y+\frac{13}{5} by the reciprocal of -\frac{4}{5}.

$$x=\frac{-5y-13}{4}$$

Solve for y

$$y=\frac{-4x-13}{5}$$

Solution Steps

Use the distributive property to multiply -\frac{4}{5} by x+7.

$$y-3=-\frac{4}{5}x-\frac{28}{5}$$

Add 3 to both sides.

$$y=-\frac{4}{5}x-\frac{28}{5}+3$$

Add -\frac{28}{5} and 3 to get -\frac{13}{5}.

$$y=-\frac{4}{5}x-\frac{13}{5}$$