Question

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

Answer 1

Answer: First Option

$y + x = 5$

Step-by-step 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 $n\neq 1$.

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

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

Answer 2

Answer:

y + x = 5

Step-by-step 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.