Solve y-2=(6-4sqrt{2})(x-1)

$$y - 2 = ( 6 - 4 \sqrt { 2 } ) ( x - 1 )$$

Solve for x

$$x=\frac{\left(2\sqrt{2}+3\right)\left(y-2\right)+2}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6-4\sqrt{2} by x-1.

$$y-2=6x-6-4\sqrt{2}x+4\sqrt{2}$$

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

$$6x-6-4\sqrt{2}x+4\sqrt{2}=y-2$$

Add 6 to both sides.

$$6x-4\sqrt{2}x+4\sqrt{2}=y-2+6$$

Add -2 and 6 to get 4.

$$6x-4\sqrt{2}x+4\sqrt{2}=y+4$$

Subtract 4\sqrt{2} from both sides.

$$6x-4\sqrt{2}x=y+4-4\sqrt{2}$$

Combine all terms containing x.

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

Divide both sides by 6-4\sqrt{2}.

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

Dividing by 6-4\sqrt{2} undoes the multiplication by 6-4\sqrt{2}.

$$x=\frac{y+4-4\sqrt{2}}{6-4\sqrt{2}}$$

Divide y+4-4\sqrt{2} by 6-4\sqrt{2}.

$$x=\frac{\left(2\sqrt{2}+3\right)\left(y+4-4\sqrt{2}\right)}{2}$$

Solve for y

$$y=2\left(\left(3-2\sqrt{2}\right)\left(x-1\right)+1\right)$$