Solve (y-1)=-1/2(x-1)

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

Solve for x

$$x=3-2y$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{2} by x-1.

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

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

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

Subtract \frac{1}{2} from both sides.

$$-\frac{1}{2}x=y-1-\frac{1}{2}$$

Subtract \frac{1}{2} from -1 to get -\frac{3}{2}.

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

Multiply both sides by -2.

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

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

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

Divide y-\frac{3}{2} by -\frac{1}{2} by multiplying y-\frac{3}{2} by the reciprocal of -\frac{1}{2}.

$$x=3-2y$$

Solve for y

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

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x-1.

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

Add 1 to both sides.

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

Add \frac{1}{2} and 1 to get \frac{3}{2}.

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