# How do you decide whether the relation 2x + 4y = 5 defines a function?

May 25, 2018

Yes it does.

#### Explanation:

A function must have one unique output in its range for each input from it domain:

$2 x + 4 y = 5$

This is an equation for a line in "standard form"; all lines are 1 to 1, i.e. they have one unique $y$ value for each $x$ value so they are all functions.

One way to be sure is to look at the graph and do the "vertical line test" if any vertical line only intersects the graph once then the mathematical expression is a function.

This can be rewritten in function notation (remember $f \left(x\right) = y$)

$2 x + 4 y = 5$

$y = - \frac{1}{2} x + \frac{5}{4}$

$f \left(x\right) = - \frac{1}{2} x + \frac{5}{4}$

graph{-1/2x +5/4 [-10, 10, -5, 5]}