Determine if each function is linear or nonlinear. Drag each function into a box to correctly classify it. linear nonlinear y=6x−2y = 3x³ + 5y=x2−33x + y = 12y = x

The linear functions are:
y = 6x - 2
x + y = 12
y = x

The non-linear functions are:
y = 3x³ + 5
y = x² - 33

Explanation:
Linear functions can be written in the form y = mx+b, where m is the slope and b is the y-intercept.  In linear functions, the x variable has at highest an exponent of 1.

The first equation, y = 6x - 2, is in slope-intercept form; it is linear.
The second equation, y = 3x³ + 5, has an x with an exponent greater than 1; it is non-linear.
The third equation, y = x² - 33, has an x with an exponent greater than 1; it is non-linear.
The fourth equation, x + y = 12, can be written as y=mx+b:
x+y=12
Subtract x from both sides:
x+y-x=12-x
y = -x+12

This is a linear function.

The fifth equation, y = x, is in the form y=mx+b; in this case, m=1 and b=0.  This is linear.