Question

Which equation is not a linear function?

Select each correct function.

a. y = xy + 2

b.y = x + 2y

c. y = -x - 2y

d. y = x - y + 2

e. y = x2 - 2 + 2y

f. y = -y + 2 - 2x

Answer 1

a, e

Step-by-step explanation:

If any of the terms has a variable with an exponent other than 1 or 0, or has a sum of variable exponents other than 1, the term is non-linear and the relation is not a linear relation.

a: the term xy has a sum of exponents of 1+1=2, so is not a linear term.

e: the term x² has an exponent other than 0 or 1, so is not a linear term.

In the attached graph, the non-linear relations are shown graphed in black. The remaining relations are all linear.

_____

Comment on linear function

By one definition, a linear function is one that is of the form

... f(x) = ax + b

Here, an equation such as y = x + 2y can be put in that form, but it is not in that form as presented. Yes, the graph is of a straight line, but you would have a hard time identifying independent and dependent variables from the equation as given.