Answer:
Given equation: [tex]2x+y=7[/tex]
Definition of a function
- A relation is a function if each y-value corresponds to one or more x-values.
- A relation is not a function if each x-value corresponds to more than one y-value.
The given function is in the standard form of a linear equation: [tex]ax+by=c[/tex]
If the given equation is rearranged to make y the subject:
[tex]y=-2x+7[/tex]
it is now in the general form of a linear equation, [tex]y=mx+b[/tex] (where m is the slope and b is the y-intercept).
A linear equation is one of a straight line, and so, by definition, each value of y corresponds to one value of x. Therefore, this is a one-to-one function.
