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

Answer:

A) $y=\frac{1}{2}x+3$ - Linear

B) $y=4x+2$ - Linear      

C) $xy=12$ - Nonlinear

Step-by-step explanation:

To determine whether a function is linear or nonlinear.

The function of a straight line is given as :

$y=mx+b$

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) $y=\frac{1}{2}x+3$

The function is in the form $y=mx+b$ and hence it is a linear function with slope $m=\frac{1}{2}$ 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  $x$

$\frac{xy}{x}=\frac{12}{x}$

$y=\frac{12}{x}$

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