For this case we have that by definition, a linear function is of the form
[tex]y = mx + b[/tex]
We have the following options:
A) [tex]1-3x ^ 2 = -y[/tex]
Rewriting:
[tex]y = 3x ^ 2-1[/tex]
It's a quadratic function!
B) [tex]y + 7 = 5x[/tex]
Rewriting:
[tex]y = 5x-7[/tex]
It's a linear function!
C)[tex]x ^ 3 + 4 = y[/tex]
Rewriting:
[tex]y = x ^ 3 + 4[/tex]
It's a cubic function.
D) [tex]9 (x ^ 2-y) = 3[/tex]
Rewriting:
[tex]9x ^ 2-9y = 3\\9y = 9x ^ 2-3\\y = x ^ 2- \frac {3} {9}[/tex]
It's a quadratic function!
E)[tex]y-x ^ 3 = 8[/tex]
Rewriting:
[tex]y = x ^ 3 + 8[/tex]
It's a cubic function!
Answer:
The linear function is option B
