Solve b-y=-mx

$$b-y=-mx$$

Solve for b

$$b=y-mx$$

Solution Steps

Add y to both sides.

$$b=\left(-m\right)x+y$$

Reorder the terms.

$$b=-mx+y$$

Solve for m

$$\left\{\begin{matrix}m=\frac{y-b}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&b=y\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-m\right)x=b-y$$

Reorder the terms.

$$-mx=-y+b$$

The equation is in standard form.

$$\left(-x\right)m=b-y$$

Divide both sides by -x.

$$\frac{\left(-x\right)m}{-x}=\frac{b-y}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$m=\frac{b-y}{-x}$$

Divide b-y by -x.

$$m=-\frac{b-y}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y-b}{m}\text{, }&m\neq 0\\x\in \mathrm{R}\text{, }&b=y\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-m\right)x=b-y$$

Divide both sides by -m.

$$\frac{\left(-m\right)x}{-m}=\frac{b-y}{-m}$$

Dividing by -m undoes the multiplication by -m.

$$x=\frac{b-y}{-m}$$

Divide b-y by -m.

$$x=-\frac{b-y}{m}$$

Solve for y

$$y=mx+b$$

Steps for Solving Linear Equation

Subtract b from both sides.

$$-y=\left(-m\right)x-b$$

Reorder the terms.

$$-y=-mx-b$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-mx-b}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-mx-b}{-1}$$

Divide -mx-b by -1.

$$y=mx+b$$