Solve y-1/2=-4/5(x+2)

$$y- \frac{ 1 }{ 2 } =- \frac{ 4 }{ 5 } (x+2)$$

Solve for x

$$x=-\frac{5y}{4}-\frac{11}{8}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{4}{5} by x+2.

$$y-\frac{1}{2}=-\frac{4}{5}x-\frac{8}{5}$$

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

$$-\frac{4}{5}x-\frac{8}{5}=y-\frac{1}{2}$$

Add \frac{8}{5} to both sides.

$$-\frac{4}{5}x=y-\frac{1}{2}+\frac{8}{5}$$

Add -\frac{1}{2} and \frac{8}{5} to get \frac{11}{10}.

$$-\frac{4}{5}x=y+\frac{11}{10}$$

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

$$\frac{-\frac{4}{5}x}{-\frac{4}{5}}=\frac{y+\frac{11}{10}}{-\frac{4}{5}}$$

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

$$x=\frac{y+\frac{11}{10}}{-\frac{4}{5}}$$

Divide y+\frac{11}{10} by -\frac{4}{5} by multiplying y+\frac{11}{10} by the reciprocal of -\frac{4}{5}.

$$x=-\frac{5y}{4}-\frac{11}{8}$$

Solve for y

$$y=-\frac{4x}{5}-\frac{11}{10}$$

Solution Steps

Use the distributive property to multiply -\frac{4}{5} by x+2.

$$y-\frac{1}{2}=-\frac{4}{5}x-\frac{8}{5}$$

Add \frac{1}{2} to both sides.

$$y=-\frac{4}{5}x-\frac{8}{5}+\frac{1}{2}$$

Add -\frac{8}{5} and \frac{1}{2} to get -\frac{11}{10}.

$$y=-\frac{4}{5}x-\frac{11}{10}$$