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Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{y-b}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&b=y\text{ and }x=0\end{matrix}\right.
Steps for Solving Linear Equation
b-y=-mx
Swap sides so that all variable terms are on the left hand side.
Swap sides so that all variable terms are on the left hand side.
\left(-m\right)x=b-y
Reorder the terms.
Reorder the terms.
-mx=-y+b
The equation is in standard form.
The equation is in standard form.
\left(-x\right)m=b-y
Divide both sides by -x.
Divide both sides by .
\frac{\left(-x\right)m}{-x}=\frac{b-y}{-x}
Dividing by -x undoes the multiplication by -x.
Dividing by undoes the multiplication by .
m=\frac{b-y}{-x}
Divide b-y by -x.
Divide by .
m=-\frac{b-y}{x}
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y-b}{m}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&b=y\text{ and }m=0\end{matrix}\right.
Steps for Solving Linear Equation
b-y=-mx
Swap sides so that all variable terms are on the left hand side.
Swap sides so that all variable terms are on the left hand side.
\left(-m\right)x=b-y
Divide both sides by -m.
Divide both sides by .
\frac{\left(-m\right)x}{-m}=\frac{b-y}{-m}
Dividing by -m undoes the multiplication by -m.
Dividing by undoes the multiplication by .
x=\frac{b-y}{-m}
Divide b-y by -m.
Divide by .
x=-\frac{b-y}{m}
Solve for b
b=y-mx
Solution Steps
b-y=-mx
Add y to both sides.
Add to both sides.
b=\left(-m\right)x+y
Reorder the terms.
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
b-y=-mx
Swap sides so that all variable terms are on the left hand side.
Swap sides so that all variable terms are on the left hand side.
\left(-m\right)x=b-y
Reorder the terms.
Reorder the terms.
-mx=-y+b
The equation is in standard form.
The equation is in standard form.
\left(-x\right)m=b-y
Divide both sides by -x.
Divide both sides by .
\frac{\left(-x\right)m}{-x}=\frac{b-y}{-x}
Dividing by -x undoes the multiplication by -x.
Dividing by undoes the multiplication by .
m=\frac{b-y}{-x}
Divide b-y by -x.
Divide by .
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
b-y=-mx
Swap sides so that all variable terms are on the left hand side.
Swap sides so that all variable terms are on the left hand side.
\left(-m\right)x=b-y
Divide both sides by -m.
Divide both sides by .
\frac{\left(-m\right)x}{-m}=\frac{b-y}{-m}
Dividing by -m undoes the multiplication by -m.
Dividing by undoes the multiplication by .
x=\frac{b-y}{-m}
Divide b-y by -m.
Divide by .
x=-\frac{b-y}{m}
Solve for y
y=mx+b
Steps for Solving Linear Equation
b-y=-mx
Subtract b from both sides.
Subtract from both sides.
-y=\left(-m\right)x-b
Reorder the terms.
Reorder the terms.
-y=-mx-b
Divide both sides by -1.
Divide both sides by .
\frac{-y}{-1}=\frac{-mx-b}{-1}
Dividing by -1 undoes the multiplication by -1.
Dividing by undoes the multiplication by .
y=\frac{-mx-b}{-1}
Divide -mx-b by -1.
Divide by .
y=mx+b
Graph
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\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.
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.
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