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6-5B Lesson Master
SKILLS
Questions on SPUR Objectives
page 2
USES
Objective B
1. slope __14 , point (8, −3)
Objective F
13. A suburban school district had an enrollment of 7,200 students in the
year 2000. Enrollment has been growing at a fairly constant rate of
50 students per year.
In 1–6, write an equation of the line given the slope and one point on
the line.
Sample answer: (0, 7,200)
2. slope −2, point (−1, 4)
a. Write an ordered pair described by the information.
y = _14 x – 5
b. Write the slope described by the information.
y = –2x + 2
3. slope −__23 , point (−6, −5)
c. Write an equation relating the number of students in the
school district y and the number of years since 2000 x.
4. slope 5, point (__25 , 12)
50
y = 50x + 7,250
d. Estimate the total enrollment the school district might expect
for the year 2010, if this rate of growth remains steady.
y = –_23 x – 9
y = 5x + 10
Sample: (0, 650)
a. Write an ordered pair described by the information.
–25
p = –25m + 650
b. Write the slope described by the information.
y = 15
y = 0.5x – 4.4
y = 5x + 10
7. The slope of a line is 5 and the x-intercept is −2. Write an
equation of the line.
y = –_13 x + _43
y = _3
8. The slope of a line is −__13 and the x-intercept is 4. Write an
equation of the line.
4
9. What is the equation of a horizontal line through the
point ( −2, _34 )?
y = _35 x + 2
10. Determine an equation for the line that contains (0, 2) and is
parallel to the line with equation y = __35 x.
In 11 and 12, the slopes of two lines are reciprocals.
_8
11. An equation of one line is y = __78 x + 1. What is the slope of the
second line?
7
c. Write an equation to represent the number of people p
in the theater after m minutes.
26 min
d. How long will it take to empty the theater?
In 15 and 16, use the table below. It represents the admission and parking
costs at a zoo when Cherise went with her family and some friends.
Everyone rode in one car and only 2 adults went to the zoo.
Parking
$6.75
Adult admission
$7.00
Child admission
$3.50
15. Let c represent the number of children who went to the zoo and
let t represent the total cost of admission to the zoo. Write an
equation relating t and c.
y = _87 x – 26
12. Find the equation of the second line if it passes through the
point (14, −10).
7,700 students
14. Six hundred fi fty people attended a dance recital. When it was over,
the theater emptied at a rate of 125 people every 5 minutes.
6. slope __12 , point (2.4, −3.2)
5. slope 0, point (−6, 15)
240
6-5B
See pages 392–395 for objectives.
16. If the total costs for parking and admission were $38.25, how many
children went to the zoo on this trip?
t = 3.50c +
20.75
5 children
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6-6A Lesson Master
SKILLS
Questions on SPUR Objectives
See pages 392–395 for objectives.
SKILLS
Objective B
In 1–5, write an equation in slope-intercept form of the line through the two
given points.
1. (1, 3) and (2, 15)
2. (−4, −8) and (1.5, 8)
3. (3, 0) and (22, −10)
4. (6, 9) and (2, 7)
y = 12x – 9
10
30
__
y = –__
19 x + 19
5. (2, 3) and (−2, 5)
y = –_12 x + 4
3. (−1.5, −0.5) and (−3, 0)
y = –_12 x
4. (5, 13) and (10, 10)
y = –_35 x + 16
y = –_13 x – 1
5. (8, −3) and (−12, 2)
y
y = –_1 x – 1
(
)
( )
y = _43 x + _53
6. −__34 , __23 and −__12 , 1
4
y = –_23 x + _53
7. Write an equation of the line through (−2, 3) and (4, −1).
x
1 2 3 4 5 6
8. Check your answer to Question 7 by graphing the line.
Copyright © Wright Group/McGraw-Hill
5
4
3
2
1
᎑5 ᎑4 ᎑3 ᎑2 ᎑1
᎑1
᎑2
᎑3
᎑4
᎑5
Objective F
7. The Blueport Bus Company finds that, if they lower their prices, more
people will ride the bus. Right now, they charge $1.25 per ride and
average 2,400 customers per day. Analysts feel that there is a linear
relationship between the cost c and the number of riders n and that if the
cost dropped to $1.00 the number of riders would increase to 2,700.
b. Use your answer to Part a to predict the number of riders if the
cost of a bus ride were lowered to $0.80.
2. (6, −3) and (22, −11)
y = 3x – 2
6. Check your answer to Question 5
by graphing the line.
a. Find an equation that relates the variables c and n.
See pages 392–395 for objectives.
Objective B
1. (2, 4) and (5, 13)
y = _12 x + 6
6
5
4
3
2
1
Questions on SPUR Objectives
In 1–6, write an equation in slope-intercept form of the line through the two
given points.
32
40
__
y = __
11 x + 11
᎑6 ᎑5 ᎑4 ᎑3 ᎑2 ᎑1
᎑1
᎑2
᎑3
᎑4
᎑5
᎑6
USES
6-6B Lesson Master
y
x
1 2 3 4 5
y = _54x + 5
9. Write an equation for the line with x-intercept −4 and
y-intercept 5.
n = –1,200c
+ 3,900
2,940 riders
10. Write an equation for the line that produced
the table of values shown below.
11. Write an equation of the line shown below.
2
1
᎑3 ᎑2 ᎑1
᎑1
᎑2
᎑3
y
x
1 2 3 4 5 6 7
᎑5
᎑6
᎑7
᎑8
y = –2x + 15
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27
y = _17 x – __
7
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6-6B
page 2
USES
Objective F
6-7A Lesson Master
USES
12. “Black Friday,” the day after Thanksgiving, is characterized by millions
of shoppers and billions of dollars in retail sales. Retail sales in 2005
were about $8.45 billion and in 2006 were about $8.96 billion.
(2005, 8.45) and
(2006, 8.96)
a. Express the data as two ordered pairs.
increase in retail sales at a rate of $0.51
billion per year
about 6%
Time (min)
y = 0.51x – 1,014.1
13. The total sales of golf equipment in the United States in 2004 were
$3,198.2 million. In 2005 the total sales were $3,474.4 million. Assume
there is a linear relationship between the number of years y since 2004
and the sales in millions s of golf equipment.
a. Express the data as two ordered pairs.
1980
580
570
560
550
540
530
520
510
500
490
480
1982
1982
1983
1984
1985
1986
1987
1988
1989
y
x
0 1 2 3 4 5 6 7 8 9 10
(0, 3,198.2), (1, 3,474.4)
Years since 1980
2. y = –8.84x + 572.81
276.2
c. Explain what the slope represents in this situation.
increase in sales at a rate of $276.2
million per year
y = 276.2s + 3,198.2
d. Write an equation for y in terms of s for this relationship.
$4,303 million
e. Use your equation from Part d to predict the total sales of
golf equipment in 2008.
1981
1. Draw a scatterplot of this data, with x being the number of years since
1980, and y the winning time in minutes.
d. What was the percent of increase in sales?
b. Find the slope of the line through these points.
Objective G
Time (min) 564.55 578.48 559.68 548.38 545.95 534.33 530.9 508.62 514.22 511.00 489.25
c. Explain what the slope represents in this situation.
e. Write an equation for y in terms of x for the relationship.
See pages 392–395 for objectives.
In 1-6, use the table below of the winning times for the men’s Ironman
World Championship triathlon in Hawaii from 1980 to 1989. (Two races
were held in 1982.)
Year
0.51
b. Find the slope of the line through these points.
Questions on SPUR Objectives
2. Use your calculator to find an equation for the regression
line for these ordered pairs. Round values in the equation
to the nearest hundredth.
3. 578.48 min in 1981
3. Graph the regression line on your scatterplot. Which time
deviates the most from the equation?
4. According to your equation, by about how many minutes does the
winning time improve each year?
5. Use your equation to predict the winning time in 2005.
8.84 min
351.81 min
6. The winner of the 2005 race was Faris Al-Sultan of Germany, who
finished the race in 8 hours, 14 minutes, 17 seconds. Did he finish
faster or slower than your equation predicted? Why do you think this
happened?
Slower; sample: Human physical limits prevent a
true linear decrease.
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Name
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6-7B Lesson Master
Questions on SPUR Objectives
6-7B
page 2
See pages 392–395 for objectives.
Objective G
In 1–7, use the table at the right of the average daily
number of passengers in January at Baltimore/Washington
International Thurgood Marshall Airport.
Year
Average Number of
Passengers per Day
2002
41,919
2003
43,313
2004
47,184
2005
46,947
1. Draw a scatterplot of these ordered pairs with x
representing the number of years since 2002 and
y representing the average daily number of airline
passengers for January.
y
2006
In 8–13 use the table below of the slugging percentage (SLG) for
Aramis Ramirez for each season from 1998 to 2006. In baseball
statistics, the slugging percentage is a measure of
the power of a hitter.
number of bases gained with hits
SLG = _________________________
number of times at bat
8. Draw a scatterplot of these ordered pairs with x
representing the number of years since 1998 and
y representing the slugging percentage.
700
47,546
SLG (thousandths)
53,000
51,000
49,000
47,000
600
500
400
41,000
1
2
3
4
1999
.250
2000
.402
2001
.536
2002
.387
2003
.491
2004
.448
2005
.578
2006
.568
4
6
8
approximately y = 0.032x + 0.319
9. Use your calculator to find an equation for the regression line
for this data.
x
0
.351
x
2
Years since 1998
43,000
SLG
1998
300
200
45,000
y
Season
5
Years since 2002
y = 1,488.8x + 42,404.2
2. Use your calculator to find an equation for the regression line for
these ordered pairs.
3. Graph the regression line on your scatterplot. By how much does
the 2005 average deviate from the linear regression equation’s
predicted average for that year?
4. According to your equation, by about how many passengers does
the daily average for January increase by each year?
5. Use your equation to predict the average daily number of passengers
in January, 2010.
6. Use your equation to find what year the average daily number of
airline passengers in January will be about 51,300.
10. Graph the regression line on your scatterplot. In which year does
the SLG deviate the most from the equation?
11. According to your equation, by about how much does Ramirez’s
SLG increase each year?
76.4
12. Use your equation to predict Ramirez’s SLG in 2007.
about 1,489
about 54,315
2001
Copyright © Wright Group/McGraw-Hill
USES
Average Daily Number of
Passengers for January
245
0.032
0.607
13. Was Ramirez’s SLG for 2006 greater or less than your equation
predicted? Why do you think this happened?
Less; sample: Human physical limits prevent a true
linear increase.
2008
7. Is the average daily number of passengers for January, 2006, greater
or less than what the equation predicted? Why do you think
this happened?
Less; sample answer: Economic factors prevent
a true linear increase.
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