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

2. Warm Up What is the linear equation for this graph? Graph y = 2x + 1
Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.

3. 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)

4. Tables: Linear or Nonlinear
Is the rate of change constant (the same)? 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

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

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

7. Identify: Linear or Nonlinear Graph?

8. Equations: Linear or Nonlinear
REMEMBER: x1 = x and x0 = 1
In “y = ” form, is x raised to a power of 1 or 0?
Does x appear in the numerator?
y = 6/x
y = x3 + 1
y = x + 4
nonlinear
y = ½ x
nonlinear
y = 4
linear
linear
linear

9. Identify:Linear or Nonlinear Equation?3x 2
y = .6x1
y = x2 + 8
y = 2/x + 5
linear
nonlinear
linear
nonlinear

10. 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.

11. Exit Slip Identify if linear or nonlinear. Table A Equation y = + 53 6 9 12 y 10 8
y = 8 x
Graph a b c

12. Practice Worksheet Complete the practice worksheet.
Work with a partner or on your own.
Submit completed worksheet for grading.
Solutions are discussed the next day.

13. 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.