GET READY BEFORE THE BELL RINGS! Take out homework and a pencil to

prepare for the homework quiz!

Check the file folder for your class to pick up graded workLocated by the bookshelf, blue crate.Look behind the tab for your class period

and take home anything with your name on it.

INVESTIGATION 2

LINEAR MODELS & EQUATIONS

Chapter 1: Thinking with Mathematical Models

2.1 MODELING LINEAR DATA PATTERNS Turn to page 31 in your textbook.

The points are not exactly in a straight line. What line would you draw as a model for the

data pattern? How would you find an equation for this linear

function?

PROBLEM 2.1 (PG 32)

Which of the two lines seems to fit the data better?

PROBLEM 2.1 B) To find out how accurate each model

is, you can calculate errors in the predictions made by the model. Those errors are the differences between the actual data and what each model predicts. Each such error is called a residual.Your turn: Complete the handouts with

tables for Figures 1 & 2

Do the residuals suggest that one model is better than the other?

HOW TO WRITE AN EQUATION FOR A LINEAR MODEL Any linear function can be expressed in

the form y = mx + b The coefficient m tells the rate at which

the values of y increase (or decrease) as the values of x increase by 1. (aka Unit Rate) It also tells steepness and direction (upward

or downward) of the graph of a function The value of b tells the point at which

the graph of a function crosses the y-axis. That point has coordinates (0, b) and is called the y-intercept.

HOW TO WRITE AN EQUATION FOR A LINEAR MODEL In any problem that calls for a linear

model, the goal is to find the values of m and b for an equation.

Turn to page 34 in your textbook

FINDING SLOPE

TURN TO PAGE 37

REFLECTION & SUMMARY What directions would you give

someone to help him or her draw a mathematical model?

Once you have drawn the line, how do you find the slope and y‑intercept?

How can you compare the accuracy of two different possible modeling lines?

REFLECTION & SUMMARY If you have to make predictions from a

linear model, which is more helpful, the equation or the line?

What are the advantages of having a linear model for your data set, rather than just a set of individual data points?

2.3 TREE TOP FUN Focus Question: What strategies do you

use in writing equations for linear function?

Review Vocabulary: Residual

Treetop Fun!

2.3 TREE TOP FUN Tree Top Fun runs adventure sites with zip

lines, swings, rope ladders, bridges, and trapezes.

The company uses mathematical models to relate the number of customers, prices, costs, income, and profit at its many locations.

TURN TO PAGE 38, PROBLEM 2.3