Solve y-(-6)=(2/4)(x-5)

$$y - ( - 6 ) = ( \frac { 2 } { 4 } ) ( x - 5 )$$

Solve for x

$$x=2y+17$$

Steps for Solving Linear Equation

The opposite of -6 is 6.

$$y+6=\frac{2}{4}\left(x-5\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$y+6=\frac{1}{2}\left(x-5\right)$$

Use the distributive property to multiply \frac{1}{2} by x-5.

$$y+6=\frac{1}{2}x-\frac{5}{2}$$

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

$$\frac{1}{2}x-\frac{5}{2}=y+6$$

Add \frac{5}{2} to both sides.

$$\frac{1}{2}x=y+6+\frac{5}{2}$$

Add 6 and \frac{5}{2} to get \frac{17}{2}.

$$\frac{1}{2}x=y+\frac{17}{2}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{y+\frac{17}{2}}{\frac{1}{2}}$$

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

$$x=\frac{y+\frac{17}{2}}{\frac{1}{2}}$$

Divide y+\frac{17}{2} by \frac{1}{2} by multiplying y+\frac{17}{2} by the reciprocal of \frac{1}{2}.

$$x=2y+17$$

Solve for y

$$y=\frac{x-17}{2}$$

Solution Steps

The opposite of -6 is 6.

$$y+6=\frac{2}{4}\left(x-5\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$y+6=\frac{1}{2}\left(x-5\right)$$

Use the distributive property to multiply \frac{1}{2} by x-5.

$$y+6=\frac{1}{2}x-\frac{5}{2}$$

Subtract 6 from both sides.

$$y=\frac{1}{2}x-\frac{5}{2}-6$$

Subtract 6 from -\frac{5}{2} to get -\frac{17}{2}.

$$y=\frac{1}{2}x-\frac{17}{2}$$