Originally Posted by

**Matt Westwood** If you write it in the form $\displaystyle y = 3x + 4$ you may find it's easier to see what's going on.

What you do is see whether you can get it in the form where $\displaystyle x$ is on its own on one side and there's a complicated manipulation of $\displaystyle y$ that you can do to get to $\displaystyle x]$.

So you have:

$\displaystyle y = 3x + 4$

Subtract 4 from both sides:

$\displaystyle y - 4 = 3x$

Divide both sides by 3

$\displaystyle \frac {y-4} 3 = x$

which can be written $\displaystyle \frac y 3 - \frac 4 3$

and it is clear that $\displaystyle x$ is a function of $\displaystyle y$.

The next one's trickier:

$\displaystyle y = \frac{2x - 3} {x - 7}$

Multiply by $\displaystyle x - 7$:

$\displaystyle y (x-7) = 2x - 3$

$\displaystyle xy-7y = 2x - 3$

$\displaystyle xy - 2x = 7y - 3$

$\displaystyle x (y - 2) = 7y - 3$

$\displaystyle x = \frac {7y - 3} {y-2}$

The only reason that's not a function is because it's not defined at $\displaystyle y=2$, and so is not one-to-one. There's no image of 2.

Can you do the third one now?