Question

Determine whether each equation below is linear or nonlinear.

Equation
y = ½ x + 3
y = 4x + 2
xy = 12
Linear or Non-Linear

Answer 1

A)
`y=(1)/(2)x+3` - Linear

B)
`y=4x+2` - Linear

C)
`xy=12` - Nonlinear

Explanation:

To determine whether a function is linear or nonlinear.

The function of a straight line is given as :

`y=mx+b`

where
`m` represents slope of line and
`b` represents the y-intercept.

Any function that can be represented as a function of straight line is called a linear function otherwise it is nonlinear.

We will check the equations given for linear or nonlinear.

A)
`y=(1)/(2)x+3`

The function is in the form
`y=mx+b` and hence it is a linear function with slope
`m=(1)/(2)` and y-intercept
`b=3`.

B)
`y=4x+2`

The function is in the form
`y=mx+b` and hence it is a linear function with slope
`m=4` and y-intercept
`b=2`.

C)
`xy=12`

On solving for
`y`

Dividing both sides by
`x`

`(xy)/(x)=(12)/(x)`

`y=(12)/(x)`

This function cannot be represented in the form
`y=mx+b`, hence it is a nonlinear function.