b, minus, y, equals, minus, m, x

Solve for b

b=y-mx

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.

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

Add y to both sides.

b=-mx+y

Reorder the terms.

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

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

-mx=-y+b

Reorder the terms.

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

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide b-y by -x.