# Is y=-3x+1/2 a function or not?

## y=-3x+1/2

Mar 9, 2018

It is a function

#### Explanation:

There are a couple of ways you can determine if an equation is a function or not.

One way is called the Vertical Line Test.

All you do here is graph the equation and look at every vertical line on said graph. If two or more points travel over that one line, it is not a function.

So let's graph $y = - 3 x + \frac{1}{2}$

graph{-3x+1/2 [-2.344, 1.981, -0.69, 1.474]}

Here we can see that only one point crosses each vertical line, making this equation a function.

Another way to solve this, if you don't have access to graph paper or utility, is to use the method of plugging in numbers for $x$ and solve. If you plug numbers in for $x$ and get different answers each time, you have a function. However, if you get the same answer for two or more numbers that you plugged in, you do not have a function.