Solve y=-xsqrt{2}+2

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

Solve for x

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

Steps for Solving Linear Equation

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

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

Subtract 2 from both sides.

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

Reorder the terms.

$$-\sqrt{2}x=y-2$$

The equation is in standard form.

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

Divide both sides by -\sqrt{2}.

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

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

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

Divide y-2 by -\sqrt{2}.

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

Solve for y

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

Solution Steps

Reorder the terms.

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