Page 1
1.
Find the equation of the line for the following set of conditions.
The slope is –4 and the line passes through the point (3,–6).
Write the answer in slope-intercept form,
y b mx=+
.
2.
Find the equation for the line through the points (–6,1) and (3,1).
Write the answer in slope-intercept form.
y b mx=+
3.
Find the equation of the line for the following set of conditions.
The the line passes through the points (–5,34) and (4,–11).
Write the answer in slope-intercept form,
y b mx=+
.
4.
Suppose the slope of a line is –5 and the line goes through the point (–6, 25).
Find the values of a, b, and c if points (–1,a), (0,b), and (–10,c) are on the line.
5.
Suppose the slope of a line is 7 and the line goes through the point (3, 20).
Find the values of a, b, and c if points (a,–43), (b,–36), and (c,–99) are on the line.
6.
Assuming that the line through the given two points has the given slope m, find the
value of t.
(8,8) and (10,t); m = 1
7.
Assuming that the line through the given two points has the given slope m, find the
value of t.
(–6,–58) and (t,–88); m = 10
8.
Find the equation for the line pictured.
Write your answer in slope-intercept form.
y b mx=+
Page 2
9.
Find a linear equation that describes the statement.
A cat is born (age 0) weighing 3.8 ounces and at 8 years of age the cat weighs 148.6
ounces.
Write your answer in slope-intercept form,
w b ma=+
, in terms of weight, w, and age,
a.
10.
Find a linear equation that describes the statement.
At the age of 7 a person is 47 inches tall and at the age of 11 the person is 55 inches tall.
Write your answer in slope-intercept form,
h b ma=+
, in terms of height, h, and age, a.
11.
By analyzing sales figures, the accountant for the Johnson Stereo Company knows that
275 units of a CD player can be sold each month when the price is $195 per unit. The
figures also show that for each $20 hike in price, 11 fewer units are sold monthly. Let x
denote the number of units sold per month and p the price per unit. Find an equation that
expresses x in terms of p.
Write your answer in slope-intercept form,
x b mp=+
. Round values to 2 decimal
places.
12.
When a large airliner approaches an airport, it begins its descent from about 100 miles
away and takes about 20 minutes to descend from an altitude of 36000 feet. Assume
that the airliner’s distance to the airport
d
is a linear function of the time, t (minutes),
since it began its descent.
A) Express
d
as a function of t (minutes). Write your answer in slope-intercept form.
B) Now find the airliner’s altitude, A, as a function of the airliner’s distance from the
airport, d. Write your answer in slope-intercept form.
13.
A small business purchases a piece of equipment for $1440. After 9 years, the
equipment will be outdated and have no value.
A) Write an equation giving the value V of the equipment as a function of t, the years
since purchased.
B) State the domain of the function. Write your answer in interval notation.
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14.
When the price is $220, a company makes 1017 bicycles available for market. For each
$4 increase in price, 17 more bicycles are made available.
Let x denote the number of bicycles available for market and p the price.
A) Find an equation that expresses x in terms of p.
Write your answer in slope-intercept form,
x b mp=+
.
B) How many bicycle will be available if the price of bicycles is set at $200?
C) What price (in dollars) should be set if 1187 bicycles are made available?
15.
A company has fixed costs of $24,000 per month and variable costs of $5.10 per unit
manufactured. (Fixed costs are those that occur regardless of the level of
production. Variable costs depend on the number of units manufactured.)
A) Find a formula that describes the total monthly costs, C, for the company as a
function of the number of units manufactured, x.
Write your answer in slope-intercept form,
C b mx=+
.
B) If the company manufactures 600 units what will their monthly costs be?
C) If the company has $27,570 available to cover the monthly costs, how many units
can the company manufacture?
16.
As a diver descends into the ocean, the pressure increases linearly with the depth (i.e.
pressure is a linear function of depth). At the surface (a depth of 0 feet) the
pressure is 15 pounds per square inch. At a depth of 33 feet below the surface the
pressure is 30 pounds per square inch.
A) Find a formula for the linear function that expresses pressure, P, in terms of depth,
d.
Write your answer in slope-intercept form and round values to 2 decimal
places, if necessary.
B) Use the function from part A to determine the pressure when the diver is 21 feet
below the surface.
Round your answer to 2 decimal places, if necessary.
C) Use the function from part A to determine how deep can the diver go if the highest
safe for his equipment and experience is 69 pounds per square inch.
Round your answer to 2 decimal places, if necessary.
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17.
In 1780, a French balloonist by the name of Jacques Charles discovered that the volume
of a fixed amount of gas held at a constant pressure is a linear function of its
temperature. In a specific experiment it is observed that if 4 liters of oxygen at 0
Celsius is warmed to 100 Celsius, the volume of the oxygen increases to 5.46
liters.
A) Determine v, the volume of oxygen (in liters) as a function of t, its temperature (in
degrees Celsius). Write your answer in slope-intercept form.
B) What is the volume of 4 liters of oxygen at 80 degrees Celsius?
C) What temperature (in degrees Celsius) is required to cause a volume of 4.2 liters?
Round all values to 4 decimal places.
18.
Jessica works at Acme Manufacturing Company. After 5 years, she was earning $16.00
per hour. After 8 years on the job, she is now earning $20.50 per hour. She has
received exactly the same annual raise each year she has been there.
A) Write a linear function describing her hourly wage, w, as a function of years
worked, y.
B) What was her beginning hourly wage?
19.
A contractor purchases a piece of equipment for $40,000. The equipment requires an
average expenditure of $4.00 per hour for fuel and maintenance, and the operator
is paid $13.00 per hour.
A) Write an equation giving the total cost C of operating this equipment for the first t
hours, including purchasing it.
B) Assuming that customers are charged $25.00 per hour of machine use, write an
equation for the revenue R derived from t hours of use.
C) Use the formula P = R – C to write an equation for the profit, P, derived from the
first t hours of use.
D) Find the number of hours this equipment must be used to break even, i.e. make a
profit of $0. Round your answer to the nearest hour.
20.
Because of a state budget crisis a publicly supported college is being forced to raise
more of its funds from private sources. Their tuition in September 2007 is $6,000;
and over the next 5 years they must gradually raise their tuition until it becomes
$9,000 in September 2012.
A) Find a linear formula for tuition, T, for any school year, s, during the period of
tuition raises. Count school years, s, starting from 2007 as year zero.
B) What is the domain of the function?
C) What is the total tuition for a student starting in September 2008 and finishing in 4
years?
D) How much more would the total tuition be if the student started a year later and
finished in 4 years?
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21.
Search and Rescue Teams are often called upon to find lost hikers in remote areas of the
Southwest. Members of the search team walk parallel to one another at a fixed
distance d between searchers through the area being searched. The team’s chance
of finding the lost person is related to the distance d of separation. The closer
together the searchers are, the better the chances of success. Based on a number of
previous searches, the following data was found to be approximately true: If d =
24 ft., P (the probability of success) = 85%. If d = 56 feet, P = 45%.
A) What is the dependent variable?
B) What is the independent variable?
C) Write the equation of the function that relates these two variables.
D) If the team is satisfied with a success rate of 75%, how many feet apart should the
searchers be?
22.
A house that sold for $35,000 in 1980 sold for $60,500 in 2000.
A) Find the average rate of change of the value of the house per year.
B) If the house continues to increase in value at the same rate, what will be its value in
2016?
23.
Determine whether the following data is linear. If it is linear, find the function and
write your answer in
y b mx=+
form. If the data is not linear, enter Not Linear.
x
–4
–1
0
3
5
24.
Determine whether the following data is linear. If it is linear, find the function and
write your answer in
y b mx=+
form. If the data is not linear, enter Not Linear.
x
3
5
6
8
10
25.
Put the following equation into y = b + mx form.
3x + 4y = –16
Page 6
26.
Find the equation of the line for the following set of conditions.
The slope is
1
2
and the line passes through the point (–15, –16).
Write the answer in slope-intercept form,
y b mx=+
.
27.
Find the equation of the line through the points (5, 8) and (–20, –12).
Write the answer in slope-intercept form.
y b mx=+
28.
Find the equation of the line with slope
2
3
and goes through the point (9, 15).
Write the answer in slope-intercept form.
y b mx=+
29.
Assuming that the line through the given two points has the given slope m, find the
value of t.
(5, 1) and (20, t); m =
3
4
.
30.
Assuming that the line through the given two points has the given slope m, find the
value of t.
(t, 5) and (–8, 2); m =
1
4
.
31.
Complete the table for the linear function.
x
f(x) = 5 + 3x
6
11
16
21
26
Page 7
32.
Find the slope of this linear function from the table.
x
f(x)
3
7
6
19
9
31
12
43
15
55
33.
Find the slope of this linear function from the table.
x
f(x)
8
–11
16
–5
24
1
32
7
40
13
34.
Put this equation into slope-intercept form.
24x + 4y = 24
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Answer Key
Page 9