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
Accepted Solution
A:
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.