1. Linear and Nonlinear Functions
Identifying functions
on tables, graphs, and equations.
Irma Crespo 2010

2. Objective: To be able to identify if a function is linear o not.
Warm-Up:

3. Linear VS NON-LINEAR Linear: The rate of change is constant (table)
The graph appears to be a straight line (graph)
Any equation that can be written in standard form
Ax +By=C (all are real numbers, and A and B are not BOTH 0)
x and y in the equation both have exponents of 0 or 1 (equation)
x and y are NOT multiplied together (equation)
x and y DO NOT appear in the denominator, exponents, or radical signs (equation)

4. Linear vs. Non-Linear: Non-Linear: The rate of change is NOT constant
The graph IS NOT a straight line

5. Tables: Linear or Nonlinear
Is the rate of change constant (the same)?
**Constant change in the x value and y value** x y 2 50 4 35 6 20 8 5 x y 1 4 16 7 49 10
100 +3
+15 +2
-15 +2
-15 +3
+33 +2 +3
+51
-15
linear
nonlinear

6. Identify: Linear or Nonlinear Table?x y 20 5 16 10 12 15 8 x 2 4 6 y 8 18
nonlinear
linear

7. Length of a Side of a Square Yard
Compare and Contrast
Yards to Feet
Number of Feet
Number of Yards
Yards to Square Yards
Length of a Side of a Square Yard
Area of Square (yd2)

8. Graphs: Linear or Nonlinear
Is the graph a straight line?
linear
nonlinear
linear

9. Identify: Linear or Nonlinear Graph?

10. Equations: Linear or Nonlinear
REMEMBER: x1 = x and x0 = 1
y = 6/x
y = x3 + 1
y = x + 4
nonlinear
y = ½ x
nonlinear
y = 4
linear
linear
linear

11. Identify:Linear or Nonlinear Equation?3x 2
y = .6x
y = x2 + 8
y = 2/x + 5
linear
nonlinear
linear
nonlinear

12. Pointers to Keep in Mind
A table is linear if the rate of change is constant.
There is a common difference.
A graph is linear if it is a straight line.
An equation is linear if the power of x is either 1 or 0 and it appears in the numerator.

13. Can non-linear functions have a slope?
What is SLOPE?
Can non-linear functions have a slope?

14. 4 types of slope (Same as Rate of Change)
Uphill, left to right
Downhill, left to right

15. Determine Slope Given a Graph:

16. Determine Slope Given a Graph:
When does it hit the next whole value!

17. If given 2 points on a line, you may find the slope using the formula
m = y2 – y x2 – x1

18. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

19. Find the slope of the line that passes through (3, 5) and (-1, 4).-4
- ¼

20. Exit Slip (NOT GRADED) Identify if linear or nonlinear. Table A
Equation x 3 6 9 12 y 10 8
y = 8 x
Graph a b c

21. Main Resources
Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Chapter 10. Columbus:McGraw-Hill.
PowerPoint created by Irma Crespo.
University of Michigan-Dearborn, School of Education. Winter 2010.