# Proving a function is continuous

I am working to prove that this function is continuous at $x = 2$

$$f(x) = 9x–7$$

To do this I know that I have to show that $\vert f(x)–f(a) \vert < \epsilon$ and that $\vert x-a < \delta \vert$

I tried to come up with a relationship between $\vert x-2 \vert$ and $\epsilon$ so I could get an appropriate number to choose for $\delta$

This is as far as I got

$$\vert f(x)–f(a) \vert < \epsilon$$
$$\vert 9x–7 \vert < \epsilon$$

I’m stuck. All of the examples the text shows give equations where it is easy to factor out the $\vert x-a \vert$ term.

A push in the right direction would be appreciated.