Question

# Determine whether the following functions are linear or non-linear and explain how you know.

Hint:

### To check if a function is linear, we check the highest degree of a term in the equation. If the highest degree of all the terms in the equation is 1, then the equation is linear, and if the degree of any terms is greater than 1, then the equation is non-linear. We check the degree of each of the terms in the given equation to check if the equation is linear.

## The correct answer is: greater than 1

*Step by step solution:*

The given equation is

We check the degree of each of the terms in the above equation.

The degree of a term is the sum of the exponents of all the variables that are present in the term. Here, the only variables are x and y.

In the left hand side, we have y.

Clearly, degree of this term = 1

In the right hand side, the first term we have is x^{3}

Degree of this term = 3

Thus, the degree of one of the terms in the equation is greater than 1.

Hence, the function is not linear.

There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Also, the graph of a linear equation is always a straight line. So, we can plot a graph of the given equation and check if it is a straight line.

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