Question

Which equation is not a linear function?

Answer 1

Answer:

a, e

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.

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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.