The document contains information about linear relationships and equations including examples about: - The cost of producing school yearbooks in relation to the number of copies purchased. - The cost of taxi fares in relation to distance traveled. - The number of bacteria remaining after an antibacterial spray is present for different time periods. - The age and price of used cars. Key concepts discussed are slope, y-intercept, domain, range, and using linear models to represent real-world scenarios.

1. Thinking
between
and
outside
the lines
A Rock Between The Lines by flickr user Jeremy Brooks

2. The cost of producing a school yearbook is $1000 for setup fees and
$1200 for each lot of 100 copies purchased. Here is a table of values
showing the total cost for 100, 200, 300, or 400 copies purchased.
(0, 1000)
Y= 12X +1000
What does the y-intercept mean? What does the slope mean?

3. Writing an equation for a line The graph below shows the cost of
taking a taxi for various distances.
What is the significance
of the y-intercept A?
What is the slope of the line?
What does the slope quot;meanquot;?
Write the equation of the line without using your calculator.
What is the cost of a 10 km trip? How far could you travel for $6.25?

4. In testing the effectiveness of a new antibacterial spray, a biochemist
recorded the number of bacteria present in a tissue culture after the spray
had been present for different periods of time. The data are recorded in
the table below:
HOMEWORK
(continues on next slide)
a) Find the slope.
(Use a regression equation.)
What does it mean?
b) Find the y-intercept.
What does it represent? c) Write the equation of the line.

5. In testing the effectiveness of a new antibacterial spray, a biochemist
recorded the number of bacteria present in a tissue culture after the spray
had been present for different periods of time. The data are recorded in
the table below:
HOMEWORK
d) After how many hours
would 25 bacteria be present?
e) State the largest value and
the smallest value of the domain.
f) State the largest value and
the smallest value of the range.

6. The following data shows the age of certain cars and their
corresponding prices:
HOMEWORK
Graph age vs.price.
Construct a scatter plot of the data.
Determine the line of best fit.
1. What is the equation of the line?
2. What is the value of the y-intercept? What is its real-world
significance?
3. What is the real-world significance of the slope?
4. Is this a good model for car prices? Why or why not?