Solve y-5=-1/6(x-4)

$$y - 5 = - \frac { 1 } { 6 } ( x - 4 )$$

Solve for x

$$x=34-6y$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{6} by x-4.

$$y-5=-\frac{1}{6}x+\frac{2}{3}$$

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

$$-\frac{1}{6}x+\frac{2}{3}=y-5$$

Subtract \frac{2}{3} from both sides.

$$-\frac{1}{6}x=y-5-\frac{2}{3}$$

Subtract \frac{2}{3} from -5 to get -\frac{17}{3}.

$$-\frac{1}{6}x=y-\frac{17}{3}$$

Multiply both sides by -6.

$$\frac{-\frac{1}{6}x}{-\frac{1}{6}}=\frac{y-\frac{17}{3}}{-\frac{1}{6}}$$

Dividing by -\frac{1}{6} undoes the multiplication by -\frac{1}{6}.

$$x=\frac{y-\frac{17}{3}}{-\frac{1}{6}}$$

Divide y-\frac{17}{3} by -\frac{1}{6} by multiplying y-\frac{17}{3} by the reciprocal of -\frac{1}{6}.

$$x=34-6y$$

Solve for y

$$y=-\frac{x}{6}+\frac{17}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{6} by x-4.

$$y-5=-\frac{1}{6}x+\frac{2}{3}$$

Add 5 to both sides.

$$y=-\frac{1}{6}x+\frac{2}{3}+5$$

Add \frac{2}{3} and 5 to get \frac{17}{3}.

$$y=-\frac{1}{6}x+\frac{17}{3}$$