# How do you decide whether the relation #3y - 1 = 7x +2# defines a function?

##### 1 Answer

You need to consider the question: **Does this relation allow for multiple values of the dependent variable for any value of the independent variable?**

#### Explanation:

For demonstration purposes I will assume that in the given relation:

The given relation can be re-arranged as

and we can see (hopefully this is obvious) that any value of

Since this was asked under the topic "Functions on a Cartesian Plane", another way to look at this is (assuming you have some way of generating the graph of this relation) is to see if there is any possibility of a vertical line crossing the line of this equation in more than one place:

In this case we can see that the graph is a straight line, so there can not be any "doubling back" to provide more than one value of