A)
- Linear
B)
- Linear
C)
- Nonlinear
Step-by-step explanation:
To determine whether a function is linear or nonlinear.
The function of a straight line is given as :
![y=mx+b](/tpl/images/0427/2501/904ac.png)
where
represents slope of line and
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=\frac{1}{2}x+3](/tpl/images/0427/2501/ef19a.png)
The function is in the form
and hence it is a linear function with slope
and y-intercept
.
B) ![y=4x+2](/tpl/images/0427/2501/68988.png)
The function is in the form
and hence it is a linear function with slope
and y-intercept
.
C) ![xy=12](/tpl/images/0427/2501/a46cd.png)
On solving for ![y](/tpl/images/0427/2501/9512c.png)
Dividing both sides by ![x](/tpl/images/0427/2501/a0e3f.png)
![\frac{xy}{x}=\frac{12}{x}](/tpl/images/0427/2501/0c400.png)
![y=\frac{12}{x}](/tpl/images/0427/2501/53448.png)
This function cannot be represented in the form
, hence it is a nonlinear function.