Beginning Algebra, 11th Edition

slope-intercept form A linear equation is
written in slope-intercept form if it is in the
form , where mis the slope and
is the y-intercept. (Section 3.4)
solution of an equation A solution of an
equation is any replacement for the variable
that makes the equation true. (Section 1.3)

solution of a system A solution of a sys-
tem of equations is an ordered pair
that makes all equations true at the same
time. (Section 4.1)
solution set The set of all solutions of an
equation is called the solution set. (Section 2.1)

solution set of a linear system The set of
all ordered pairs that satisfy all equations of
a system at the same time is called the solu-
tion set. (Section 4.1)
solution set of a system of linear inequal-
ities The set of all ordered pairs that
make all inequalities of a linear system
true at the same time is called the solution
set of the system of linear inequalities.
(Section 4.5)
square of a binomial The square of a
binomial is the sum of the square of the
first term, twice the product of the two
terms, and the square of the last term:
and

. (Section 5.6)

square root The inverse of squaring a
number is called taking its square root. That
is, a number ais a square root of kif
is true. (Section 8.1)
square root property The square root
property (for solving equations) states that if
, with , then or

. (Section 9.1)
squaring property The squaring property
(for solving equations) states that if each
side of a given equation is squared, then all
solutions of the given equation are among
the solutions of the squared equation. (Sec-
tion 8.6)

standard form of a complex number The
standard form of a complex number is

. (Section 9.4)

standard form of a linear equation A
linear equation in two variables written in
the form , with AandBnot
both 0, is in standard form. (Section 3.4)
standard form of a quadratic equation
A quadratic equation written in the form
, where a,b, and care
real numbers with , is in standard
form. (Sections 6.5, 9.1)
straight angle A straight angle measures
180°. (Section 2.4)

subscript notation Subscript notation is

a way of indicating nonspecific values.

In and , 1 and 2 are subscripts on the

variable x. (Section 3.3)

subset If all elements of set A are in

setB, then Ais a subset of B, written.

(Appendix)

substitution method The substitution me-

thod is an algebraic method for solving a

system of equations in which one equation is

solved for one of the variables, and then the

result is substituted into the other equation.

(Section 4.2)

sum The answer to an addition problem is

called the sum. (Section 1.1)

sum of cubes The sum of cubes,

, can be factored as

. (Section 6.4)
supplementary angles (supplements)
Supplementary angles are two angles whose
measures have a sum of 180°. (Section 2.4)
system of linear equations (linear system)
A system of linear equations consists of two
or more linear equations to be solved at the
same time. (Section 4.1)
system of linear inequalities A system
of linear inequalities consists of two or more
linear inequalities to be solved at the same
time. (Section 4.5)

table of values A table of values is an

organized way of displaying ordered pairs.

(Section 3.1)

term A term is a number, a variable, or the

product or quotient of a number and one or

more variables raised to powers. (Section 1.8)

terms of a proportion The terms of the pro-

portion are a,b,c, and d. (Section 2.6)

three-part inequality An inequality that

says that one number is between two other

numbers is called a three-part inequality.

(Section 2.8)

trinomial A trinomial is a polynomial con-

sisting of exactly three terms. (Section 5.4)

union The union of two sets AandB, writ-

ten , is the set of elements that belong

toeither A or B, or both. (Appendix)

universal set The set that includes all ele-

ments under consideration is the universal

set, symbolized U. (Appendix)

unlike terms Unlike terms are terms that

do not have the same variable, or terms with

the same variables but whose variables are

not raised to the same powers. (Section 1.8)

variable A variable is a symbol, usually a

letter, used to represent an unknown number.

(Section 1.3)

vary directly (is proportional to) yvaries

directly as xif there exists a nonzero real

number (constant) ksuch that. (Sec-

tion 7.8)

vary inversely yvaries inversely as xif

there exists a nonzero real number (constant)

ksuch that. (Section 7.8)

Venn diagram A Venn diagram consists of

geometric figures, such as rectangles and

circles, that illustrate the relationships among

sets. (Appendix)

vertex The point on a parabola that has the

leasty-value (if the parabola opens up) or the

greatest y-value (if the parabola opens down)

is called the vertex of the parabola. (Sec-

tions 5.4, 9.5)

vertical angles When two intersecting lines

are drawn, the angles that lie opposite each

other have the same measure and are called

vertical angles. (Section 2.5)

vertical line test The vertical line test states

that any vertical line will intersect the graph of

a function in at most one point. (Section 3.6)

volume The volume of a three-dimensional

figure is a measure of the space occupied by

the figure. (Section 2.5)

whole numbers The set of whole numbers

is. (Sections 1.1, 1.4)

x-axis The horizontal number line in a rec-

tangular coordinate system is called the

x-axis. (Section 3.1)

x-intercept A point where a graph inter-

sects the x-axis is called an x-intercept. (Sec-

tion 3.2)

y-axis The vertical number line in a rec-

tangular coordinate system is called the

y-axis. (Section 3.1)

y-intercept A point where a graph inter-

sects the y-axis is called a y-intercept. (Sec-

tion 3.2)

zero-factor property The zero-factor pro-

perty states that if two numbers have a product

of 0, then at least one of the numbers is 0.

(Sections 6.5, 9.1)

Z

Y

X

5 0, 1, 2, 3, 4,Á 6

W

y=kx

y=kx

V

A ́B

U

a

b=

c

d

T

1 x+y 21 x^2 - xy+y^22

x^3 +y^3 x^3 +y^3 =

A 8 B

x 1 x 2

aZ 0

ax^2 +bx+c= 0

Ax+By=C

a+bi

x=- 2 k

x^2 =k k 70 x= 2 k

a^2 =k

x^2 - 2 xy+y^2

1 x+y 22 =x^2 + 2 xy+y^21 x-y 22 =

1 x,y 2

1 0,b 2

y=mx+b

Glossary G-5