# How do you decide whether the relation y = - 7 / 2x - 5  defines a function?

The first indication that this expression might be a function is that it has a dependent variable ($y$) and an independent one ($x$). If you graph this function, the result will be a straight line, as it doesn't have exponential or logarithms related to $x$:
One of the definitions of a function is that, for every $x$ value, there can only be 1 $y$ value corresponding.