Linear Vs nonlinear from table

Linear Vs nonlinear from table

Review

• If given a graph you are looking for a straight line (straight= constant rate of change)

• If given an equation you are looking for something that could be written in y=mx+b form (it may not be in this form but we can rewrite it this way)

When given a table you are looking for a constant rate of change (ROC)

• ROC is calculated $\frac{change\ in\ y}{chnage\ in\ x}\ or\ \frac{y_2-y_1}{x_2-x_1}$  

• Make sure all the row have this same ROC

• If even one differs, then its NOT linear

Practice

row 1 and 2: (4-1)/(1-0) =3

row 2 and 3: (7-4)/(2-1)=3

row 3 and 4 (13-7)/(4-2) =6/2 =3

row 4 and 4 (16-13)/(5-4)=3

All the same so its linear!

Practice

row 1 and 2 (25-20)/(2-1)=5

row 2 and 3 (33-25)/(3-2)= 8

They are NOT the same so its nonlinear

You do not need to find all the rows, as soon as it differs you are done.

More examples!

Check yourself

Multiple Choice

Is this function linear or nonlinear?

• linear function

• nonlinear function

Multiple Choice

Is this function linear or nonlinear?

• linear function
• nonlinear function

Multiple Choice

Why is this function linear?

• This is a linear function because the y-intercept is (0,2)
• This is a linear function because it forms a curved line.
• This is a linear function because is does not have a constant rate of change.
• This is a linear function because is has a constant rate of change.

Multiple Choice

Why is this function linear?

• This is a linear function because it does not have a constant rate of change
• This is a linear function because it creates a curved line.
• This is a linear function because it have a constant rate of change.
• This is a linear function because it's y-intercept is (0,2)

Multiple Choice

Why is this function linear?

• This is a linear function because it does not have a constant rate of change
• This is a linear function because it creates a curved line.
• This is a linear function because it have a constant rate of change.
• This is a linear function because it's y-intercept is (0,2)

Multiple Choice

Is this function linear or nonlinear?

• linear function

• nonlinear function