Lesson 15, Section 2.5 (part 2)
More Application Problems:
1)In 1997, 10% of the homes in the U.S. had more than one (multiple) computers. By 2001, this percent had increased to 24.4%. Let t represent the number of years since 1997 and P(t) represent the percent of U.S. homes with multiple computers. Assume that this data is a linear pattern.
a)Write the appropriate data points (t, P)
b)Find the rate of change (slope).
c)Write a linear function, P(t) = mt + b
d)Use your linear function to predict what percent of U.S. homes had multiple computers in 2005.
e)Use your function to predict what year the percent of homes with multiple computers is about 50%.
f)If this trend continues, when will all U.S. homes have multiple computers?
2)In 1999 about 48 million Americans used the Internet to find some travel information. By 2003, that number had grown to about 64 million Americans. If N(t) represents the number (in millions) of Americans using the Internet to find some travel information and t represents the number of years after 1999, find the following.
a)Find a linear function to fit this data.
b)What does the slope of this function represent?
What does the y-intercept of this function represent?
3)Suppose that 6.5 million pounds of coffee are sold when the cost is $8 per pound, and 4.0 million pounds are sold when it is $9 per pound. Let p = number of pounds sold (in millions) and C = cost per pound.
a)List the data points (p, C) for this data.
b)Find a linear equation for these data points.
c)Use this linear equation to predict how many pounds will be sold when the cost is $6 per pound.
Parallel & Perpendicular Lines:
Parallel lines are lines in the same plane that do not intersect.
Perpendicular lines are lines in the same plane that intersect at 90 degree angles.
Describe whether the following pairs of slopes would make the lines parallel, perpendicular, or neither.
ABCD
4)Determine if the following two lines would be parallel.
Line 1: contains the points (12, -2) and (-6, 7)
Line 2:
5)Determine if the following two lines would be perpendicular.
Line 1: contains the points (1, 1) and (-2, 2)
Line 2:
6)Given a linear function
a)Find the slope of any parallel line.
b)Find the slope of any perpendicular line.
For this group of problems, find the equation or function for each line described.
7)Line contains the point (1, 4) and is parallel to the line .
8)Line contains the point (-3, -2) and is perpendicular to the line .
9)Line contains the point (0, -7) and is perpendicular to the line .
10)Line contains the point (5, -2) and is perpendicular to the line y = 6.
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