# Changing the subject of the formula

When changing the subject of a formula, we mean to rearrange the formula so that we have a different subject. To do this, we must remember:

Change side, Change operation

In other words, if you move a term from one side of the equals sign to the other, we change the operation to do the opposite. For example, if the term you want to move is adding, then when you move it to the other side it subtracts.

Question

The general equation for a straight line is $$y = mx + c$$. Rearrange this formula to make $$c$$ the subject.

First, rewrite the equation so that you have $$c$$ on the left hand side.

$mx + c = y$

Next, move the $$mx$$ to the other side and as you can see, this term is adding at the moment, so when it moves to the other side of the equation it does the opposite – subtracts.

$c = y - mx$

Question

The formula used to calculate the volume of a prism is $$V = Ah$$. Rearrange this formula to make $$h$$ the subject.

First thing to do is rewrite the equation so that you have $$h$$ on the left hand side.

$Ah = V$

Now you can see that $$A$$ is multiplying $$h$$, so when you move it to the other side, it does the opposite operation, so it will divide.

$h = \frac{V}{A}$

Question

Change the subject of the formula $$d = 4t -7$$ to $$t$$.

$d=4t-7$

$4t - 7 = d$

$4t = d + 7$

$t =\frac{d+7}{4}$