Question

Decide whether y is a function of x.
2x + y = 7

Answer 1

2x + y = 7, y is a function of x

Step-by-step explanation:

2x + y = 7 is a function

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Rewrite into slope intercept form

y = 7 - 2x

y = -2x + 7

• It is a linear equation (straight line)

The vertical line touches the graph only one time. Thus y is a function of x.

Answer 2

Given equation:
`2x+y=7`

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:
`ax+by=c`

If the given equation is rearranged to make y the subject:

`y=-2x+7`

it is now in the general form of a linear equation,
`y=mx+b` (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.