Question

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

Answer 1

This is a linear function.

Explanation:

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`:
graph{(-7/2)x-5 [-10, 10, -10, 10]}
With the graph plotted, you can make the vertical line test. Draw multiple vertical lines across the graph. If they always touch the function in only one spot, then it is a function.
One of the definitions of a function is that, for every `x` value, there can only be 1 `y` value corresponding.