Math CentralQuandaries & Queries


Question from Leigh, a student:

Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=y-mx. Could you please assist me with this

Hi Leigh,

An equation is like a balance with the balance with the balance point at the equal sign. You are allowed to manipulate the equation (balance) in certain ways as long as you maintain the balance. The manipulations that are allowed is to add the same amount to both sides of the equation or multiply both sides of the equation by the same amount. Thus, for example, if you have

\[y = x - 3\]

then you can add 3 to both sides to obtain

\[ y + 3 = x - 3 + 3\]


\[y + 3 = x.\]

With the example you give, $ y = mx + b$ you can add $-mx$ to each side to obtain

\[y - mx = mx + b - mx\]


\[y - mx = b.\]

Since $y - mx$ balances with $b,$ $b$ balances with $y - mx$ and thus

\[b = y - mx.\]


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