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

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.

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

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

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

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)

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.

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

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

Linear or Non-Linear? linear Non-linear linear Non-linear C F 32 5 41 32 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