College Mathematics: Learning Worksheets Chapter 1
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Name ________________________________ Date ______________ Class ____________
Goal: To solve linear equation and linear inequalities
In Problems 1–3, solve for the variable:
1. 78228
xx
+= +
Section 1-1 Linear Equations and Inequalities
Equality Properties: 1. If
x
yand a is any real number, then .
x
aya
x
x
x
x
2. If
x
yand a is any positive real number, then ax ayand
.
x
y
aa
3. If
x
yand a is any negative real number, then ax ayand
.
x
y
aa
Interval Notation: A bracket, ] or [, is used if the endpoint is included.
A parentheses, ) or (, is used if the endpoint is not included.
Infinity, either positive or negative, always uses a parentheses.
2. 7 3(6 11) 167
yy
3. 810
63
mm
+= +
4. 9422
x
+>
5. 52113
6212
x
x
−<− +≤
−<− ≤
6. 35
34 24
12 3(12) 12 5(12)
uu
uu
3
7. Break-even Analysis. A publisher for a promising new novel figures fixed costs
(overhead, advances, promotion, copyediting, typesetting, and so on) at $87,000 and variable
costs (printing, paper, binding, shipping) at $4.50 for each book produced. If the book is sold
to distributors for $28 each, how many must be produced and sold for the publisher to break
even?
Let x = the number of books produced. Since the break-even point is the point when cost is
the same as the revenue:
College Mathematics: Learning Worksheets Chapter 1
College Mathematics: Learning Worksheets Chapter 1
Name ________________________________ Date ______________ Class ____________
Goal: To find the equations of lines, x-intercepts, and y-intercepts
In Problems 1–12, write the equation of the line in slope-intercept form with the given
characteristics:
1. Slope is 8 and y-intercept is (0, 3).
2. Slope is –5 and y-intercept is (0, 6).
Section 1-2 Graphs and Lines
Slope of a Line: 21
21
,
y
y
m
x
x
−
=
− where
111
:,Pxy and
222
:,Pxy
Slope-Intercept Form of a Line: ,
y
mx bwhere m is the slope and (0, b) is the y-intercept.
y
3. Slope is 3
7 and passes through the point (–14, 2).
11
()
yy mxx
−= −
4. Slope is 4
5
and passes through the point (2, –3).
11
()
yy mxx
5. Passes through the points (4, 8) and (8, 4).
21
48 4 1
yy
mxx
−−−
====−
81(4)
84
12
yx
yx
yx
−=− −
−=−+
=− +
6. Passes through the points (–1, 4) and (2, –2).
21
24 6 2
yy
mxx
7
7. Passes through the points (0, 6) and (5, 0).
21
06 6
yy
mxx
6
0(5)
5
66
5
yx
yx
8. Passes through the points (0, –6) and (1, 0).
21
21
60 6 6
01 1
yy
mxx
−−− −
====
−−−
9. A horizontal line that passes through the point (–2, 8).
10. A horizontal line that passes through the point (2, –5).
11. A vertical line that passes through the point (–2, 7).
12. A vertical line that passes through the point (2, –8).
College Mathematics: Learning Worksheets Chapter 1
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13. 3 3
y
x 14. 2 2
y
x 15. 11
2
y
x
3(0) 3
y
2(0) 2
y
1(0) 1
y
16. 44
3
yx
17. 3 3xy
4(0) 4
y
03 3
y
9
18. Graph each line in Problems 13–17.
Graph for 13 Graph for 14 Graph for 15
Graph for 16 Graph for 17
10
19. A piece of equipment used in a landfill has an original value of $200,000. After two
years of use, the piece of equipment is valued at $150,000.
a) If the depreciation of the equipment is assumed to be linear, find an equation to
relate the value (V) of the equipment over time (t).
b) What would the value of the piece of equipment be after 6 years?
c) In how many years would the value of the piece of equipment be $0?
Solution:
a) Since the value started at $200,000 and after two (2) years it was worth
$150,000, the equipment depreciated as follows:
b) Substitute 6 in for t:
c) Find the value of t when V = 0.
College Mathematics: Learning Worksheets Chapter 1
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Name ________________________________ Date ______________ Class ____________
Goal: To interpret slopes and find linear regression equations
In Problems 1–3, use the given information to answer the questions.
1. Depreciation. A new car worth $45,000 is depreciating in value by $5000 per year.
a) Find the linear model for the current value of the car, v, and the number of
years, y, after it was purchased.
b) Interpret the slope of the model.
c) If the car is 3 years old, what does the model predict for its value?
d) After how many years will the car be worth nothing?
Solution:
Section 1-3 Linear Regression
Solving Real-World Problems
1. Construct a mathematical model.
3. Interpret the solution.
Linear Regression on a Graphing Calculator
2. In the “STAT” mode, find the “LinReg” function.
College Mathematics: Learning Worksheets Chapter 1
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2. Health Club Membership. A health club offers membership for a fee of $59 plus a
monthly fee of $15 per month.
a) Find the linear model for the membership fee, f, and the number of months, m,
since you have been a member.
b) Interpret the slope of the model.
c) If you have been a member for 24 months, what does the model predict for the
fee you have paid so far?
d) After how many months will you have paid the health club $329?
Solution:
13
3. Stress. The table below shows the relationship between a stress test score and the
diastolic blood pressure for 8 patients. A linear regression model for this data is
0.56 41.71,yx=+
where x represents the stress test score and y represents the blood pressure.
Stress Test Score, x 55 62 58 78 92 88 75 80
Blood Pressure, y 70 85 72 85 96 90 82 85
a) Interpret the slope of the model.
b) Use the model to predict the blood pressure for a person with a stress test
score of 75
c) Use the model to estimate the stress test score for if the diastolic blood
pressure was 90.
Solution:
a) For every 1 point increase in the stress test score, the diastolic blood
b)
0.56 41.71
yx
c) 0.56 41.71
yx
College Mathematics: Learning Worksheets Chapter 1
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