Question

Which function is a linear function?

Answer 1

For this case we have that by definition, a linear function is of the form

$y = mx + b$

We have the following options:

A) $1-3x ^ 2 = -y$

Rewriting:

$y = 3x ^ 2-1$

It's a quadratic function!

B) $y + 7 = 5x$

Rewriting:

$y = 5x-7$

It's a linear function!

C)$x ^ 3 + 4 = y$

Rewriting:

$y = x ^ 3 + 4$

It's a cubic function.

D) $9 (x ^ 2-y) = 3$

Rewriting:

$9x ^ 2-9y = 3\\9y = 9x ^ 2-3\\y = x ^ 2- \frac {3} {9}$

It's a quadratic function!

E)$y-x ^ 3 = 8$

Rewriting:

$y = x ^ 3 + 8$

It's a cubic function!

Answer:

The linear function is option B