Math 142–Rodriguez
Lehmann–2.2
Finding Equations of Linear Models
A. Finding an equation of a linear model by using data described in words
1. Turn the data given into ordered pairs.
y − y1
m= 2
2. Find the slope m using the slope formula.
x2 − x1
3. Choose one of the points.
4. Use the slope and the chosen point to find the equation that models the data.
Note: In this section we are only finding an equation that describes the relationship
between the variables given. It is in the next two sections that we actually use the
equations to answer some questions.
Ex 1: For Pacific albacore tuna, the weight and mercury concentration are approximately
linearly related. A 4-kilogram tuna has an average mercury concentration of 0.10 part per
million. A 10-kilogram tuna has an average mercury concentration of 0.19 part per million.
Let c by the average mercury concentration (in parts per million) of a Pacific albacore tuna
that weighs w kilograms. Find an equation of a linear model to describe the data.
Ex 2: Sales at duty-free shops worldwide have increased approximately linearly from $2.0
billion in 1980 to $34.0 billion in 2007. Let S be sales at duty free shops (in billions) in the
year that is t years since 1980.
Ex 3: The number of unruly airline passengers per year has decreased approximately
linearly from 279 passengers in 2003 to 141 passengers in 2007. Let n be the number of
unruly passengers in the year that is t years since 2000. Find an equation of a linear
model to describe the data.
B. Finding equations of a linear model by using data displayed in a table
1. Create a scattergram. Do this on a graphing calculator.
2. Determine if there is a line that comes close to the data points. If so, choose two
points you can use to find the equation that will model the data. The points you
choose do not have to be data points but to keep things simple, we will always use
data points.
3. Now that you have chosen two points, follow the steps from the previous problems
to find an equation.
4. Use a graphing calculator to verify that the equation you found comes close to the
points in the scattergram.
Let’s practice choosing “good” points. Then we will find an equation of the line.
Lehmann – 2.2
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Lehmann – 2.2
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