1. Linear and Nonlinear Relationships

2. Learning Target
I can determine whether a table, equation, or graph represents a linear or nonlinear relationship.

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. Definition of Linear Relationship
When graphed, a linear relationship will create a straight line. There will be no curve or bend in the line.
Linear relationships have a constant rate of change (slope).

5. Definition of Nonlinear Relationship
When graphed, a nonlinear relationship will NOT result in a straight line. The graph may be curved, U-shaped, or V-shaped.
Nonlinear relationships do NOT have a constant rate of change.

6. How to Identify Linear/Nonlinear Relationships
You can look at an equation, a graph, or a table of x and y values and determine whether the relationship is linear or nonlinear. The following slides will explain how to tell the difference between linear/nonlinear.

7. Equations- Linear or Nonlinear?
Linear Equations:
All linear equations will either be written in the form or y=mx+b, or they can be rearranged into that form.
The “x” value can only have an exponent of 1 or 0 in linear equations.
If there is no exponent written above the “x,” the exponent is assumed to be 1.
If there is no “x” present in the equation, the exponent for “x” is 0.
“X” cannot be in the denominator.
“X” cannot be an exponent.
“X” cannot be in a radical sign (Square Root).
“X” and “y” cannot be multiplied together.
“Y” must also only have an exponent of 1 or 0.

8. Equations- Linear or Nonlinear?
Nonlinear Equations:
In most nonlinear equations, “x” will have an exponent of 2 or higher.
If “x” is in the denominator, the equation is nonlinear.
If the equation cannot be written in the form of y=mx+b, it is nonlinear.

9. 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

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

11. Graphs: Linear or Nonlinear?
Linear graphs will ALWAYS be a STRAIGHT LINE.
The straight line can be:
Vertical
Horizontal
Diagonal

12. Graphs: Linear or Nonlinear?
Nonlinear graphs will NOT be a straight line.
Nonlinear graphs may be:
Curved
U-Shaped
V-Shaped

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

14. Identify: Linear or Nonlinear Graph?

15. Tables: Linear or Nonlinear?
Linear Tables:
A table is LINEAR if there is a constant rate of change.
What does that mean?
If the “x” values in the table increase or decrease by the same amount each time AND the “y” values in the table increase or decrease by the same amount each time, the table is linear.

16. Tables: Linear or Nonlinear?
Nonlinear Tables:
A table is NONLINEAR if there is NOT a constant rate of change.
What does that mean?
If the “x” values in the table DO NOT increase or decrease by the same amount each time and/OR the “y” values in the table DO NOT increase or decrease by the same amount each time, the table is NONLINEAR.

17. 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

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

19. 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