Question

Which of the following equations represents a linear function.

Answer 1

C. y =
`(1)/(2) x + 9`

Explanation:

A linear function is a straight line, with the highest degree of the function being 1. That means you are looking for the function where x is to the first power, which is just x.

And as x would be the highest degree, the only other possible term in the equation would be a constant.

In A, x is to the -1 power.

In B, x is to the 3rd power.

In C, x is to the 1st power.

In D, x is to the 2nd power.

Therefore, as x is to the power of 1 in choice C, y =
`(1)/(2) x + 9` represents a linear function.

Answer 2

No equation shown in A through D is linear.

Explanation:

For an equation to be linear, you must have all variables alone or just multiplied by a number. You cannot have variables multiplying other variables, variables in a denominator, variables raised to a power of 2 or more, variables in a root sign, or a variable as an exponent.

A. variable in denominator: not linear

B. variable raised to the 3rd power: not linear

C. variable as an exponent: not linear

D. variable raised to the 2nd power: not linear

Answer: No equation shown in A through D is linear.