1. Section 3.1 Understanding Linear Trends and Relationships
Definitions:
Linear Relationship:
a direct relationship between the y-coordinate and the x-coordinate
all the points on a graph of a linear relation lie along a straight line

2. Linear Trend: a trend in which the relationship between two variables follows a linear pattern.
Positive Trend: when one variable increases as the other increases.
Negative Trend: when one variable increases as the other variable decreases.

3. Line of Best Fit
a straight line that represents a trend in a scatter plot that follows a linear pattern.

4. Non-Linear Relationship:
No direct relationship between the y-coordinate and the x-coordinate
the points on a graph of a non-linear relation do not lie along a straight line
SUMMARY

5. Independent Variable
the variable being changed
graphed on the x-axis
Dependent Variable
the result when the independent variable is changed
graphed on the y-axis
Y axis – Dependent Variable
X axis – Independent Variable

6. Problem #1
To observe growth or behavior patterns, scientists measure and tag birds and other animals. Mario measures the height and wingspan of 12 geese. He wonders if there is a trend in the relationship between the two variables that will allow him to make a reasonable prediction of the wingspan when he knows the height.
Describe how to set up the axes of a graph to display the data.
- the top row is graphed on the x-axis (independent variable)
- the bottom row is graphed on the y-axis (dependent variable)

7. The data forms a straight line – linear.
b) Create a scatterplot of the data. What do you notice about the pattern in the points?
The data forms a straight line – linear.
As the height of the geese increases the wingspan increases.

8. Describe the trend in the relationship between the two variables
Describe the trend in the relationship between the two variables. Is it positive or negative, or is there no trend?
- positive trend
Draw the line of best fit. Describe how well the line represents the trend in the relationship between the variables.
- Most of the points are very close to the line of best fit and this shows a strong relationship between the independent and dependent variables.
e) Predict the wingspan of a goose that is 100 cm tall.
- 165 to 170 cm

9. Section 3.1 Comparing Linear and Non-Linear Relationships
REMEMBER
A linear relationship is a direct relationship between the y-coordinate and the x-coordinate. All the points on a graph of a linear relation lie along a straight line.
This means the independent and dependent values change at a constant rate.
Calculating Rate of Change
Independent Variable
Distance (km)
Cost ($) 60
100 80
200
300
120
400
140
Dependent Variable
+100
+20
+20
+100
+100
+20
+100
+20

10. Linear or Non-Linear? linear Non-linear linear Non-linear C F 32 5 4132 5 41 10 50 15 59 20 68
Amps
Watts 5 75 10
300 15
675 20
1200 75 9 9
225 9
375 9
525
linear
Non-linear
Time
Bacteria 1 20 2 40 4 60 8 80 16
100 32
Dollars
Tax 60 3
120 6
180 9
240 12
300 15 3 1 2 3 4 3 8 3 16
linear
Non-linear