Intermediate Algebra (11th edition)

122 CHAPTER 2 Linear Equations, Inequalities, and Applications

STUDY SKILLS

Your textbook provides material to help you prepare for quizzes or tests in this course.
Refer to a Chapter Summaryas you read through the following techniques.

Chapter Reviewing Techniques

N Review the Key Terms and New Symbols.Make a study

card for each. Include a definition, an example, a sketch

(if appropriate), and a section or page reference.

N Take the Test Your Word Power quizto check your under-

standing of new vocabulary. The answers immediately

follow.

N Read the Quick Review.Pay special attention to the head-

ings. Study the explanations and examples given for each

concept. Try to think about the whole chapter.

N Reread your lecture notes.Focus on what your instructor

has emphasized in class, and review that material in your

text.

N Work the Review Exercises.They are grouped by section.

✓Pay attention to direction words, such as simplify,

solve, and estimate.

✓After you’ve done each section of exercises, check

your answers in the answer section.

✓Are your answers exact and complete? Did you in-

clude the correct labels, such as $, cm^2 , ft, etc.?

✓Make study cards for difficult problems.

N Work the Mixed Review Exercises.They are in mixed-

up order. Check your answers in the answer section.

N Take the Chapter Test under test conditions.

✓Time yourself.

✓Use a calculator or notes (if your instructor permits them on tests).

✓Take the test in one sitting.

✓Show all your work.

✓Check your answers in the back of the book. Section references are provided.

Reviewing a chapter will take some time.Avoid rushing through your review in one
night. Use the suggestions over a few days or evenings to better understand the mate-
rial and remember it longer.

Follow these reviewing techniques for your next test. Evaluate how they worked
for you.

Reviewing a Chapter

3.1

ordered paircomponents

originx-axis

yrectangular (Cartesian)-axis

plotcoordinate system

coordinatequadrant

graph of an equation

linear equation in twofirst-degree equation

standard formvariables

yx-intercept-intercept

3.2

runrise

slope

3.3

slope-intercept form point-slope form

scatter diagram

3.4

linear inequality in twovariables

boundary line

3.5

dependent variableindependent variable

relationfunction

domainrange

function notation3.6

linear functionconstant function

KEY TERMS

1 a, b 2 ordered pair a specific value of x

(read “x-sub-one”)

x (^1) Greek letter delta
mslope
≤ function of x(read
“ƒ of x”)
ƒ 1 x 2
NEW SYMBOLS
1.An ordered pairis a pair of
numbers writtenA.in numerical order between
B.bracketsbetween parentheses or brackets
C.between parentheses in whichorder is important
D.between parentheses in whichorder does not matter.
2.A is an equation that can be written inlinear equation in two variables
the formA.
B.C.
D.
3.An A.interceptis
ythe point where the -axis intersect x-axis and
B.a pair of numbers written betweenparentheses in which order matters
C.a coordinate systemone of the regions determined by
Axy=+xBy=C.
ax= 2 b
Ax+By (^6) C
D.the point where a graph intersectsthe

4. x-axis or the y-axis.
   The A.the measure of the run over theslopeof a line is
   B.rise of the linethe distance between two points
   C.on the linethe ratio of the change in
   change in xalong the lineyto the
   D.the horizontal change comparedwith the vertical change between
   two points on the line.
   5.A A.relationis
   B.a set of ordered pairsthe ratio of the change in
   change in xalong a lineyto the
   C.the set of all possible values of
   D.the independent variableall the second components of a
   set of ordered pairs.
   6.A A.functionthe pair of numbers in an orderedis
   pair

B.a set of ordered pairs in whicheach x-value corresponds to

C.exactly one a pair of numbers writteny-value

D.between parenthesesthe set of all ordered pairs that

satisfy an equation.

7.The A.the set of all possible values ofdomainof a function is

B.the dependent variable a set of ordered pairsy

C.the difference between the x-values

D.the set of all possible values ofthe independent variable

8.The rangeof a function isx.

A.the dependent variable the set of all possible values of

B.a set of ordered pairsy

C.the difference between the y-values

D.the set of all possible values ofthe independent variable

x.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

SUMMARY

CHAPTER 3

1.C; Examples: 2.D; Examples:

x-intercept is and the y-intercept is .4.C; Example:The line through 3.D; Example:In FIGURE 4(b)of Section 3.1,the

The set defines a relation.6.B; The relation given in Answer 5 is a function.and has slope 5.A; Example:

the domain is the set of x-values, .8.A; Example:In the function in Answer 5, the range is the set of 7.D; Example:In the function in Answer 5,

y-values,. 5 0, 3, 6 6

(^5) 2, 4, 6 6
51 2, 0^12 3, 0, 1 4, 3^22 , 1 6, 6 26 1 0, 2^21 3, 6 2 1 5, 4 2 45 - - (^63) =- 22 =-1.
1 0, 3 2 , 1 3, 8 2 , 1 4, 0 (^23) x+ 2 y=6,x=y- 7
CHAPTER 3Summary 199