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

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

or

\[y + 3 = x.\]

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

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

or

\[y - mx = b.\]

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

\[b = y - mx.\]

Penny