Determine whether each equation below is linear or nonlinear.
equation
y = ½ x + 3
y = 4x + 2
xy = 12
linear or non-linear

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 :

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)

The function is in the form and hence it is a linear function with slope and y-intercept .

B)

The function is in the form and hence it is a linear function with slope and y-intercept .

C)

On solving for

Dividing both sides by  

This function cannot be represented in the form , hence it is a nonlinear function.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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