How are all linear equations functions?

Question

How are all linear equations functions?

Answer 1

except for x = constant

all linear equations are functions because for each x value there is only one y value

for x = constant, for each x there are many y values... in fact this is a vertical line.

To test a function you can use the vertical line test, If the vertical line crosses the line in 2 or more points, then the equation is not a function

Answer 2

by definition

Answer 3

All linear equations of the form y = mx + c NOT INCLUDING VERTICAL LINES are functions because every x-value only yields one y-value, which is consistent with the definition of a function.

Answer 4

They aren't:

x = 4 is a linear equation, but it is not a function!

(it graphs as a vertical line, and therefore fails the Vertical line test)

points on the line repeat x-values... (4,2) and (4,-2) are both on the line

Answer 5

One way to identify a function is if the x-values do not repeat. If you look at a graph of a linear equation, you'll see that the the x-values will never repeat. Therefore, all linear equations are functions.

I hope this helps!

Answer 6

By definition, yes