Question

Which of these functions is a linear function? y + x = 5 y + x2 = -2 y = 2x3 + 1 3x2 + y2 = -4

Answer 1

y + x = 5

Explanation:

The graph of
`y+x=5` is a straight line

The graph of
`y+x^2=-2` is a parabola.

The graph of
`y=2x^3+1` is a non-linear curve.

The graph of

`3x^2+y^2=-4` is an ellipse.

A graph of a linear function is a straight line.

Therefore y + x = 5 is the correct choice.

Answer 2

Answer: First Option

`y + x = 5`

Explanation:

The linear functions have the following form

`ax ^ n + bx ^ m = c`

Where a and b are constants and are real numbers and the exponent n and m is always equal to 1.

`m=n=1`

In other words, the linear equations have the form

`ax + by = c`

Identify among the options the functions that have this form

`y + x = 5` is a linear function with
`a = 1`,
`b = 1`,
`c = 5` and
`m=n=1`

`y + x^2 = -2` is not a linear function because
`n\\eq 1`.

`y = 2x^3 + 1` is not a linear function because
`n\\eq 1`

`3x^2 + y^2 = -4` is not a linear function because
`n\\eq 1` and
`m\\eq 1`