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Question 369064: Are all linear equations functions? Is there an instance when a linear equation isnot a function? Please give me support to know the difference.
Found 2 solutions by Fombitz, neatmath:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Equations of the form  are not functions.
Those are vertical lines and fail the vertical line test.
But all linear equations of the form  are functions.
Answer by neatmath(302)  (Show Source):
You can put this solution on YOUR website! All linear equations EXCEPT one certain kind are indeed functions!
In order to have a function, you must have a one to one correspondence between the x values and the y values.
In other words, for ANY given x value, there can be one and only one specific y value.
All linear equations except one certain kind adhere to this one to one correspondence rule.
You can verify that a linear function (or any function) is indeed a function by using the Vertical Line Test.
Basically, if you draw a vertical line through any given part of the graph of the function, the vertical line will cross the graph of the function in at most one place.
It is possible it will not cross the graph at any point depending on the function, but for linear functions, the vertical line will cross the graph at one point only (except for that one certain kind of exception I mentioned above).
Have you guessed what the exceptions are?
The only linear equations which are NOT functions are vertical lines themselves!
Any linear equation in the form x=a where a is some constant number is NOT a function.
Some examples of these linear equations which are not functions are:
x=0
x=2
x=-700
x=1/3
Specifically they are NOT functionc because for a given x value such as x=a, there are an infinite number of possible y values.
In addition, the functions of the form x=a also fail the Vertical Line Test!
All other linear equations which are not in the form x=a ARE indeed functions.
I hope this helps!
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