1. y x
Linear vs. Non-linear

2. Definitions
Function
Linear
Non-Linear

3. It’s easy when you have a graph!x
Linear - straight line
It’s easy when you have a graph!
Non-linear - not a
straight line

4. Which of these are linear?y x
Which of these are linear? A. B. C. D.

5. As x changes, is the change in y a constant change?
Is it a linear function?
Using a table... x 2 3 4 5 y 6 8 10
X - input
Y - output
As x changes, is the change in y a constant change? x -1 1 2 y 5 6 7 8 x 1 3 5 7 y 9 25 49

6. Linear or Non-Linear? x 1 2 3 4 y 5 10 17 x -2 -1 1 2 y 3

7. With an Equation?
A linear function always can be represented in the format: y = mx + b
Special note: the x has to have an exponent of 1 to be a linear function!
y = .5x + 9
y = 2x - 8
y = 3x2
y = 5 - x2

8. 1. A linear function is a straight line.
In summary...
1. A linear function is a straight line.
Yes:
No:
2. A linear function will represent a constant rate of change.
Yes:
No:
3. The formula is in the form of y = mx + b.
**It will not have any exponents.
Yes: y = 3x + 5
y = 4x
y = 2x - 7
No: y = x² + 4
a = 3b² - 4
y² = 2x³

9. Final Practice! 1. Which one is a linear function? A. B. C. D.
2. Which ones are linear functions?
A. y = x B. 2y = 4x C. y = 3x² + 2
3. Match the table to the correct function:
A. 2x² B. 2x² C. 2x D. 2x - 2 x 1 2 3 y 4 10 20
Is the function above linear or non-linear?