Solve for b

b=y-mx

$b=y−mx$

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.

${m=xy−b ,m∈R, x=0b=yandx=0 $

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.

${x=my−b ,x∈R, m=0b=yandm=0 $

Solve for y

y=mx+b

$y=mx+b$

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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.

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

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

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

Divide both sides by -m.

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

Dividing by -m undoes the multiplication by -m.

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

Divide b-y by -m.

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

Subtract b from both sides.

-y=-mx-b

Reorder the terms.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

y=mx+b

Divide -mx-b by -1.