Chapter 2

• Using lines to model data

• Finding equation of linear models

• Function notation/Making predictions

• Slope as rate of change

2.1 Using lines to model data

• Records were taken over a period of 5 years of the numbers of baby girls born in Linea Hospital. The data is shown in the chart below.

Year Baby Girls

2005 413

2006 482

2007 502

2008 565

2009 641

Scattergram

• A graph of plotted ordered pairs

• Should include:– scaling on both axes– labels of variables and

scale units

Num

ber

of g

irls

born

Approximately Linearly Related

• Sketch a line that comes close to (or on) the data points

• There are multiple lines that will reasonably represent the data.

Definitions

• Approximately linearly related – a set of points in a scattergram of data that lie close to/or on a line

• Model – mathematical description of an authentic situation

• Linear model – linear function, or its graph, that describes the relationship between two quantities in an authentic situation.

Making Predictions with Linear Models

• Approximately how many babies will be born in 2010?– 708

• When were 500 babies born?– Sept 2006

When to Use a Linear Function to Represent Data

Scattergrams are used to determine if variables are approximately linearly related. Warning: Draw the line that comes close to all data points, not the greatest number of points

Intercepts of a model• Let t be the years after

1950, let p be the polar bear population.

• Sketch a linear function to describe the relationship

• What does the p-intercept represent?– Population of 24,000 polar

bears in 1970

• When will the polar bears become extinct?– 2015

Years Since 1970

10 20 30 40

4

12

20

p

t

For a function with independent variable t :

– interpolation :

when part of the model used whose t-coordinates are between the t-coordinates of two data points

– extrapolation: when part of the model used whose t-coordinates are not between the t-coordinates of any two data points

more faith

losing faith

losing faith

no faithmodel breakdown – when prediction doesn’t make sense or estimate is a bad approximation

Modifying a model• In 2005, there were 6, recorded polar bears

• Modify to show the population leveling out at 8,000 polar bears.

• Modify to show polar bears becoming extinct.

Group Exploration

• p 62-63

Quiz

• Vocabulary

• Identify independent/dependent variable

• Find the equation of a line given a graph or graph the line give the equation

• Change an equation to slope intercept form

• Determine if lines are parallel, perpendicular or neither.