n. By6:00 P-'ol..the tempenllure had risen 11r. Bymidnighllhe tempeolture hadlallefo tr. What was the temperature 8t midnight?
606 Chapter 22 Chapter ReviewfreSl
Show You Undent.n.d From looking at the ab$OIule Y8Iue of an integer. coo)'OU tell...tlether lIlal integer ispositive ornegative?
..,.. ..
Extra Practice
Set A ~l,llP_ _1)
Write the opposite ofeach integer. Then write the absolute value 01 each inleger.
1. '5 8. -72
". -10
7. '100 12. '31
3. "7 ... '89
14. '66
10. '55
1$. -64
Set B (lMocw'l2.pp.reH91)
Draw 8 number line from -8 to +8 and label each Integer. Write>,<, or = lor each • .
5. -8 _ +8
2. +3. '5
8. +6. +7
Write the integers in order Irom least to greatest.
10. '5. '8. -4, -5 13. -5. O. +5. -7 Set C (I..-:>n5. 1lPã5liIe-(!()')
Decide whether tile answer will be positive or negative.
Then use the number line to add or subtract.
I I I I I I I I I I I I I I I I I I I I I I
, I I
-, -, o " "
1. '4 + '5
5. '9 - '6
13,+9+-9
2. '6 + -8
10.-8++3
14. '2 - +8
3.-11+'7
11.+6+-5
18,-6++9
I ExtraPracbCta1 edupIace.comIl!IaIl I Chapter 22 ExIra Practice 607
.e Use What You Know
Use this page to review and remember what you need 10 know for this chapter.
VOCABULARY
Choose the best word to complete each sentence. Vocabulary
lunctlon
2. A{n) _ _ is a rule that gives exactly one value ofy lor each value of x.
1. The number'S is a number. ortIeredpel,
oppolllte positive
CONCEPTS AND SKILLS
COmpare. Use the number line. Write>,<.or '" lor each • • -8 -7 -6 -5 ~ ~ ~ -\ 0 '\ '2 ~ '4 -5 ~ '7 '8 3. - 8 . - 6 4 . 0 . - 5
Add orsubtract. You may use the number line above If you wish.
e. '4 + -8 8. -5+'S
.-=- ~
.... ""' """.- .•
10. Describe the pattern in the values of x
and yin the function table below.
• ,
• '"
, "
, , , " factsPractice.Seepage659
HandsOn
Integers and the Coordinate Plane
Ob;&Ctive 0,,,,,,,ordemdpairsinlh8lcoJrquad'anl'ofIh<I COOfdir>a16 plane.
Vocabulary
eoordlfllltep l _
"....Ia )"3.la quedrant orderedpelr origin eoordlflllt8a Learn About It
Constell3lions are grOtJps of stars that appear together in the sky. You can poftray constellations on a coordinate plan.e.
A coordinate plane is formed by two perpendicular lines called axes. that lie in the plane. The horilontal axis;s called the x-axis. The vertical axis is called the ,..axls. These axes divide the plane into 4 quadrants, numbered I, II. III. and IV.
Some of the stars for the constellation Hercules are mapped on the COOrdinate plane at tile right.
What ia another way to describe the location01 the alar at point A?
Materials gOd pape'
-
You can describe any locationon the plane by using an ordered pair (x, yj.The point named by the ordered pair (0, 0) is the origin_
o To reach pointA, move left from the origin 10 -2 arld up to +4.
o The numbers -2 arld +4 are the coordinates 01 point A
~
SOlution: The location of the slar at A is given as (-2, ã4) in Quadran! II.
Other Examples
A. Point In Quadrant IV
• Po4nl 0 is in OJadrantlV.
• To raach point D.start at the origin. MoYe right 2 units and down 2 units.
• Po4nlDisat{ã2,-2).
610
B. Dlatance Between Polnta
• Po4nlAisat{ 2,4}andpointEisat(-2, 5).
• For two pointa. il the x-coordinates or the y-coo<dinates ale the same, you can counl to lind the distance between those two points.
• The distance beIWlHln Aand Eia 9 units.
~~.
/ Always start81theotIgin. " ' MowIe1lOfrightalongthe '" x-ui.lirs1,then upOfdown ~
... alOngtheJ'"uis. - ' Here is tlowto use ordered pairs
to representttle major stars in the constella~on Volans. or the Flying Fish,
Plot the star located at po;nt V(-S. '3),
• Start at the origin (0, 0).
• Goleft to 8 and up to '3.
• Mark a po;nt at ( 8, '3). Label it V.
To pIotlhe other stars in Volans. copy the graph and use these OIOOfed pairs.
('3. -3) _ (righl 3, down 3) _ ('6.'3) _ (nghI6, up3) _ (0. '2) _ (00 move, up2) _ (-3. '4) - 0 - (18113, up4) - 0 -
('7. 1) - 0 - (nghI7,downl)-o-
-, .,.N
po<nl L po<n1 0 po<ntS
,
•
,
, •
••
...
Guided Practice M\c. Yourself
Use the coordirtate plane below for E~ercises1-6.
Write the ordered pair for each point.
1.L 2.M 3.N
, Do I~leftOfr\gl1 from0 to lind the xã
coordif>alo?
Write the letter name of each point.
"
"
-fE -1'
-,"'; i
.L-l- i! J
, • '"•
. ~~!"'
• •
• .,
"
,w ,.
8.8('2. *2)
12. Wand M Use the coordinates to plot each point.
Lobel each point with Its letter.
Find the distsnce between each pair of points.
11. XandZ
Explain YourThinking'" Is the location (-2. '3) the same as ('3. -2)?
Why or why not?
Chapter 23 Lesson 1 611
Practice and Problem Solving
•
•
Use the graph 01 the Big Dipper and Litlle
•
Dipper asler;sms'or E~erc;ses13-24. , ,
Write the ordered pair for each point. ,
u. 8 ... 0 • • •
F I •
". ". •
u. K ". L • •,
Write the leller name 01 each point. ,
". (-8. -1) ~. n. -4) ••
(-2. -7) (+3. -6) DJ~ •
". ". • " .R
Find the distance between each pair 01 points. •
23. G and H 24.ZandF
Use grid paper. Piol points using the coordinates for stars In the constellallon called the Whale, or the sea Monster.
Label each point wllh Its letter.
". A (-12. +5) ~. B(-11. +8) ". C(-9.+8) ~. 0(-9. +4) ". E(-8. +2)
~. F(-4.0) ". 6(0. -4) ". H(+4. -4} ". 1(+10. -S} ~. I n . -9)
". K(-2. -10) ". L (-11. -4) ". M('l. -7) ". N('6.-S}
". Connect pointsA-L in order. Then connect Lto Eand Mto J. Can you see the whale?
Which point represents the eye of the whale?
Jt Algebra. Expressions Use grid paper. Plot each point when m ,,2 and n ,,3.
40. P(m+ 1.n-2) 41. Q(m-5,n+6} 42. R(m-8,n-3) 43.S(m+7.n+S)
Solve.
Write About II Draw your own constellation on grid POpel" List the ordered pairs. Write instructions for drawing your constellation.
46. The constellations Taurus. Cygnus. and Draco look like a swan. a dragon. and a bull. Cygnus is not a bull or a dragon.
Taurus is not a dragon. Match each constellation to its animal.
45. What pattern can you find in this group of ordered pairs: (0. 0). ('1. +2).
(+2. +4). (+3. +6). (+4. +8). (+S. +10)?
47. The COOrdinates of each point in Quadrant I are always positive: (+. +).
Write rules for the coordinates in Quadrants II. III. and IV. Explain why your rules work.
612
Multiple Choice ~
50. In which quadrant would the I
ordered pair(-3, <2) appear?
(Ch.23.~I)
Mixed Review and Test Prep Opftn Response
Evaluate each expression, when a= 2, b= 4, and c= 3.Write >,<, or = to compare. pi.5, ~61
48.2 x (b-a). (a+ b)';' c
4~. (b x c).;. a . (10 + a) + a
A'
B III
<I,
D,V J
Where's the Spaceship?
2 Players
What You'll !'feed • grid papoer'coloredpoend15
How to Play
The first player to lind all the other player's spacecratt wins the game.
• Space shuttle
• Space slation
•
.. ,
•
."
•
Atter each attempt. tell the player it the spacacratt was located or give a hint by telling whether the spacacratt is above, below. to the lett 01. or to the right of the named point.
Each player draws a coordinate plane on a sheet 01 grid paper aJld labels the ..ãaxis Irom -to to
, I0 and ttle y-axis trom -10to '10.
The object of the game is to find each others spacacraf1, Players take tums naming coordinates to try to locate the other playe(s spacacralt.
EaCh plBy(!r marks the location 014 spacecraf1 on the graph withoot showing the other player.
Each spacecraf1 should be located at a dilferent pair 01 coordinates .
• Satellite
• Spaceship
o o o
o
Chapter 23 Lesson 1 613
Integers and Functions Vocabularylunetlon
Learn About It
You learned that a function relates the value of two variables. such as)< and y. For each value of x, there is exactly one related value ofy.
Kirsten ordered some space posters. Each poster cost $2,
and there was a shipping charge of $3 per order.
COS 8 Of rsensa ,.
I
~t~.. Make a functiolllaDle with x and y .'" Substitute each value ofx
0 roumnslor the function y - 2,.+ 3. 0 into the function to lind Use the numbers 1 through 4 !ofx. ltIe value 01 y.
y ..21<+3 1"'21<+3
, , , ,
, , • " 1)+3F 2+3
, , ,
"
2)'" 3 ,.,
, , ,
" 3)'" 3 ,.,
, ,
" " 4) • 3 ,.,
Po$dive 5(;llIl oo~
',::."118<"1 as . 50'7
y=2x+3
" 1 ,
total cost number 01 shipping posters ordered cost
Make 8 lunelian table to show the possible lotal t l K l t rde
The total cost of Kirsten's order is a function of the nllmbel"
of posters she orders. She can use the equation y = 2x+ 3.
where xis the number of posters ordered. b '
- .. (\.
Think
,. , ,. ,
ExtraHeIil ateduplace.comJmap 10 - 6
,-, ,-,
-2 - 6
~~
y z x_6
, ,
" ,
, , , -,
, •
Integers as yalues
In a tunction, the Yalues tor xand y also can be negative.
Substitute tofind y.
Another Example
614
Guided Practice ~\(. Yourself
Complete the function table.
1. Function:y= 3 - x
• ,
, , ,
0
2. Function: y= 2x
• , , , ,
"
• DidI subsliMe !he correct value 10<thevariable?
• can I ... a panem that willhelpmeliodtoorule?
Explain Your Thinking'" Why is it helpfulto organize the x- andy-~alues in a function table?
Practice and Problem Solving
.
• , , ,
,
0 5 y" 5x
.
• , , ,
, ,
4 y=x-5
• ,
-, ,
0,
Complete the function table.
3y=x+5
Sol~e.
6. The cost for souvenir star chatts is $12 each plus $5 shipping per order. Make a table to show the total cost for
ordering 1.2,3,4, or 5charts.
a. Kif\(putsmoney in his savings account each month and his father then adds $5.
Write a function to describe how mudl money is put intheaccount each month.
1. Togelher Bob and Deb scored 28 points. Bob scored 4 more points than Deb. How many points did each person score?
II. Who will win the game? Jodi started with 17 points. lost 6. and gained 4.
Sara started with 11 points, gained 8.
and lost 2.
" . 6 ... 1 ,
&Ira PractICeSee page 627.set6
14. The functionAnne's age(8) IIIa" eterms of+-4 expr~ Earl~~e II
(e). How aid will Anne beWhen~E'"
is27? Explain howyoo found your
answet'. fCI>.23.l.-=w>2)
Chapter 23 Lesson 2 615 Mixed Review and Test Prep I.
f Open Response
Muillply or dl~lde.p, 12. ~2-3. ~
10.~xi 11.10~xf
Objective Grapll an eq..ation on. coordinate plane.
Use Functions and Graphs
,
"
.. •
• ,
• • • , •
,
• , , ,
{', 5) (2, 7) (3, 9)
• ,
, ,
, , , ,
Learn About It
You can use both iI function table Ilnd II graph to show the corresponding x-and y-values of a function rule.
In the last lesson. you saw thaty = 2x + 3 shows lhe total cost (yj lor the number of posters (x) that Kirsten ordered.
You can graph y = 2x + 3 to show the possible total costs for different ordefS.
y =2x+3 Ordered Pair
Notice 1ha\ since all values forx and yare positive. only the first quadrant of the coordinate plane is shown.
You can also graph funC\ioos that involve negative numbers.
To do that. you need to show all quadrants of the coordinate plane.
Graph Ihe equation y = x - 2 on a coordinate plane.
.'" Make a function table. .'" Graph each ordered pair.
0 0 ,
Rule:y .. x-:z •
• ,
~, , ,
, , ,
~ ~, , ~ • " , , " .
, , ~,
0 , k!'
, , ~,
Since xcan bea
• Inlet'" ormi,1IdnumbIlr, a linecanbedrawfl./
616
You can also use the graph 01 a function to predict what other pairs may be included in the function.
Graph the equation y = II - 2 on a coordinate plane, using the values -2 to 2for II. Use the grtlph to predict the value of y when II= 5.
<tillã... Ma~e a funclk>n ta~e. Rule:y .. x - 2
0 , , • • ,
0, , ,
, 0
<tI,e... Graph each ordered pair. .'" Extend the line. Read the yvaloe
0 e where ttle line crosses the xvalue 5.
, TIl:
• I
, , ,
. .
! . . . • • . .
, ,
•• ã
•
I
• •
-
Solution: Fory - II 2. whellllis 5.y IS 3.
Guided Practice M\t YOurself
Find values of y to complete each function table.
Then graph each function on grid paper.
1. y""I1-2
• ,
, ,0
2. y=II+3
• ,
,
0,
3.y-2I/-1
• ,
0,
,
• DidIsubslit.,.e each value!ofIIin Ih8 equationtolind )'?
• Did I grapl1lhe equation
8$a straiglU line?
Explain Your Thinking . . How could extending the graph in EJ<ercise 3 help ~
you find the value for y when II = -2? ~
Chapter 23 Lesson3 617
Practice and Problem Solving
Find values of yto complete each function table.
Then graph each equation as a strslghtllne on grid peper.
4. y"x-1
• ,
-, ,
0,
s.y"x+4
• ,
-, ,
-,
0
II. y"3x-2
• ,
0,
, ,
7.y"3x+1
• ,
0,
, ,
Find three ordered pairs for each function.
Then use them to graph Ihe function as a stralghiline.
8. y"x+ 1
12. y=2Ji
Solve.
lI.y"x-4 13.y=4x
10. y"x+6 14.y=3x-l
1l.x-S"y 15. y=2Ji+2
18. Graph y= 2xam:!Y - 4xas straight lines on the same COOrdinate plane. How are the graphs alike? How are they different?
Write About It Graphy = x - 2 and Y" x + 2 as straight lines on the same
coordinate plane. How are the graphs alike?
How are they different?
18. Explain how you can use the graph at the beginning of this lesson to find how much it would cost Kirsten for 6 posters.
111. Plot 3 or more points in a straight line on a coordinate plane, Find an equation fOf the line. Ask a partner to check the equation.
Mixed Review and Test Prep Open Response
Multiply or divide.10>. 13,~2--6;
O'l, 14,~4-7)
20.8 x 0.8
22.4 ... 0.8
618
21.0.4 x 0.05 23. 2,6'"0.07
Multiple Choice
24. Which of these ordered pairs is JlOt a solution for y" 4x+ 2?
P'L23.t.e.on3)
c (0. 2) D (1, 6) ExtraPracticeSee page 627.SetC
Social Studies Connection Where in the U.S.A.?
Mapmakers use a system very similar to a coordinate grid to identify positions of places on Earth. latitude O' is at the equator. latitudes are North (N) or South (5) of IIle equator.
longitude O' passes through Greenwich.
England. longitudes are either West (W) or East (E) of 0'.
2. New Orleans. LA
5. Use a map or an atlas.
Find the latitude and longitude for where you live.
4. los Angeles. CA
Estimate the latitude and longitude for each city.
I. Boston. MA
3. Denver. CO
-
-
,. . .. .' . •
-
., ....~
Find what city is nearest each location.
7. 4SãN, lOQ"W 8. 40ãN. 110"W
10. Explain the differences and similarities of locating and labeling a point on the coordinate plane and locating and labeling a city on a map.
WHKlVG)RUDER eduplKe,~
Cheek your understanding of Lessons 1-3.
1.W 2.X 3.Y
Make II table lor each luncllon. Use 1/ = D, 1, 2, and 3.
Write the ordered pairs and then graph the lunction.
<L-2and3l
4.y'"I/-4 s.y-2x 8.y-2x+1
<,
, , •
Chapter 23 lesson 3 619
Problem-Solving Application
Use a Graph
Objective U...graph.to ... probklms.
Distance Traveled by Light Sometimes youneed 10 read the
data In/I graph to solve II problem.
Howlong does it take light 10 travel the mean distance 0193.000,000 miles 'rom the Sun to Earth?
The original graph is shown in black.
Since 93,000,000 miles ;s not shown on the graph, the graph was exler.OOd as shown in red.
Thln~: 93million rriles Ost>e_
9O ...1Iion and 100 rTdion miles.
'00
A hna is drawn horizontally Irom
about 93.000,000miles unlil it meets 1 z 3 • S II 7 II a 10 Itle graph. Then II vertical line is TI... (",Inul••j
drawn to lind the time.
Solution: It takes abou18~minutesforliglttotravelfromtheSunto Earth.
Sometimes you need to display datil in II graph
Number of
10 help you solve II problem. People (Xl Cost(y!
One planetarium uses the table al the right to ,
"
delermine the cost tor II group \0 see IIshow.
3 "
H<lW much would it cost tor II group 019 people? , .n
STEP 1 Use the table to write Ofdered pairs.
(2. 7): (3. 9): (4, III $howCosts
STEP 2 Graph the given coordinates.
I "
STEP 3 Ederldtho graph with coordinatosfor
"
5 through 9 people. as shown in red. !
"
Solution: The cost tor 9 pooplo is $21. ! "
•
,,:. S""ceyoucannolt>aYll ""'" ,
• parIat ape<s<>n,onlylhol poinls ) ,
ar..grapll9dfor a>Unbng •
' - oombers 2through 9. . / , , , • • , , • •
""milo.01 ...
620
Guided Practice
UN the graphs ancllM latHon page620 lor Problems 1-2.
I. Ittakes lightabouI6 minutes10reach Venus from theSun, Abou! howfar from theSun isVenus?
2. Using thedata from thetable and its gl'llph.
write an equation that relaleS the number of people to the tOlaI cost of admission lor the group.
<@> Theequation It y - (• • ~ + •.Lookat
the graph. tf you extend the graphto the y-alCis, what Is the value 01 ylor It - O?
Independent Practice
...~.
3- The giltshop ill theplaneurium mal1ls up thecost ~ model solarsystems as shoYm in the table. Write 811equation 10show how10 fond the storeprice(rl ~any modelsolarsystem It costI(
•. SoWetheequation you wroIe in Problem 3 10find the storepric:e lora model that costs $120.
._, ,.
do,_?
Coo. &~. . . .
"" ""
'" ""
"" ...
... .ro
Comparing Weights on Earth and Mars
5. The grapl1at the left shows the
relatlollship !letweell all object's weight
011 Earth and its weight011 Mars. Suppose a rocll. weighs 15 potJnds on Mars. About
how much would that same rock weigh
on Earth?
6. 00 Earth an awonaul weighs 118
pounds.. About how much would that.
astronaut weigh ifshe landed OIl Mars?
1, Martha says that the eqoation
'epIesenting thedata in the graphis
Y _ 41( "yistheweight on Earth and x
is the weighton Man. isMartha correa?
Explain your reilsorWng.
Chapler 23 Leuon 4 621
Obj&Ctive kl9ntilyand ....saibe lransklrmalions inIt>&
coordIM1Q plane.
Transformations in the Coordinate Plane
Vocabulary
t.anlJ.tlon
,.."'.. ,~"oo J
r.rle<:tlQn .oUlllon
Materials 000","n81" grid scissors
• On Miranda's map, her tlome is at point (0, OJ.
She leaves home amI walks west 3 blocks and north 5 blocks. Where is she? What translations take her \0 this point?
Remember that a translation slides a point or figure 8 given distance in a given direcliOfl.
Learn About It
Find Miranda'lllocatlon after moving 3 blocks _sl and 5 blocks north.
, -
. . 0, ãi-:! •. •
...."
Afler walking 3 blocks west, Miranda is at IX'inl (-3. 0). Walking 5 blocks north PUIS her at (-3, '5).
Solution: Miranda is at her school.
_. •
Try this activity to translate ligures and points on a cOOfdinate plane.
to1lr... Draw a rectangle in Quadrant!. ,
0
tol~... Trace the rectangleOf] Mother sheet
-+t-t-
0 of paper and cur il 001.
toll;... Translate Ihe reclangle and lrace it • . .
0 • •
~11f" Reoord the coordinatesforeach Yllrtex.
0 .,
EFt • •
~11f.. Describe lhe lranslation you made.
0 •
A trans/ormation ;s a change in the position of a figure on a graph.
Transformations include translations, reflections, and rotations.
622
Reflections and Line Symmetry
•
• •
•
,
, , . ? H"ã
... A rellectlon is a flip 01 a figure that results in a mirl'Of image.
Name the coo.-dinates of poinlS Aand 8 Use a reflection to docide whether the alter a reflection across the y-axis. ligure has line symmetry.
=+:!
Rellect each YertElJC across the y-axis.The
newpoints will be the same diStanoo10the left oItlla y-axis as Aand8 are to its right.
The newpoints will be (-3,6) and(-2, 2).
II an axis isa line 01 symmetry, thlffi erther its xã or y' coordinates will be opposites.
f'Qint A(-3, 2) is opposite f'Qint 8 (3, 2).
Point C (-5, -3) is opposite Point D (5, -3).
Rotations and Rotational Symmetry
... A rotalion isa tum arounda given point.
Name the coo.-dinates of point Aafter a hall-turn around the origin.
~ turn 000 ~ turn laoo
i turn 270' 1turn . 360°
A ligure has rotational symmetry ~ it looks exactly the same alter being rotated less than 360ãaround a center point. When the hgure turns 90", rt looks the same. The flQl.lre has rotational symmetry.
Traoo the axes. mar\<. point A. and turn the tracing 1SO'.
. !~If: o. A¥A=
o ,
'0: •
Chapter 23 Lesson 5 623
Guided Practice
Use the diagram. Name the coordinates 01 triangle LMN after the transformations.
1. Translate the triangle left 3 units. then down 1 unit 2. Reflect the triangle over the x-axis.
3. Rotate the triangle a~ turn about (0. 0).
Write line. rotational. or both
to describe the symmetry 01 the ligure.
., •
•
.,
• ,
•• •
•
• DidImoYIIeach point in tileCOfrect
llirection?
Explain Your Thinking" Does a transformation change the shape of the original figure? Explain.
Practice and Problem Solving Use the diagram. Name the coordinates 01 triangle RSTafter each translormatlon.
15. Translate right 4. then down 1.
7. Reflect over the y-axis.
8. Rotate at turn clockwise about (0. 0).
II. Reflect over the y-axis. Then rolale counterclockwise a quaner tum around (0, 0).
Write line, rotational, or both to describe the symmetry of each figure.
,
•
•
13. TriangleABCwas translated left 3 units and up 1 unit II ended up at A(2. 4), 8(2, 6). and C (6. 6). What were the original coordinates?
624 ExtraPracbce seapage627,setD.
Mixed Review and Test Prep -
Open Response
Simplify.[Ol. S, ~61 :2$. If you rotate trapezoid MNOP 180"
counterclockwise. what would be
... (7 + 19) - 32 ". 20 + 82 _ (15 + 10) its new coordinates? P>.23,~51
• • "
... 4+3x6-12 H . (15 - 8) x (24 +-6)
.. 5x3+6J ". 18+2x5-3 • ,
15-22 +6 •
w. ". (10+8) x 2 +12
• • •
". 9X(10-2)+3 ". 3O-5x4-2 • •
". (19-9)X~ ". 7'-2 X 8 + 27 .,
J
Visual Thinking Trans Sym Club
Can you discover the names of the members of Trans Sym Club?
'OW
How do you think the members decided on aname for their club?
Chapter 23 Lesson 5 625
.e Chapter Review/Test
VOCABUlARY
1. One of lhe lour legionsin a coordinate plane Ionned bythe coordinate axesiscalel:! a(n)----,
2.. AfIgUre thai is flipped Olfef I ~oe shows a(nl-"
3. The _ is!hepoint at which the ...-axis andy-axis of a
coordio8te plane intersee:l
4. A(n) __ is. figure thai is IUmedabout I given poinL CON CUTS AND SKILlS
Usethe coordinlltes to plotand label each point on gridplOpe!'•.-on',,,,,,8.~'3t
Vocabulary
-qo . . . .
s, R( 3. '3)
•. O{*4. *4)
I. M(ã2. 2) 10. 0(0. '3)
7. P(-2, -4) 11. 1('4, -3)
.. H(5.0) 12. 5( 3, 2)
,
,)I~
D E
"'3 "? -,-,0 '1"'1"3.
7,
Find 4 ordered pairs lor each function. Then UN them 10 graph each functlon.~2..:1.,pp.15.oHj'lIl
13.y-x+4 14.y_II_5 1,.y-2x+1
Use Iha diagram. Name the coordinate. olt,llOglI DEF altar Iha Ir.n,formatlons. ' - -is.llJI.~
11. Translate righl4 units.
II. Rotate at turn clod<wiseabout (0. 0).
II. Reflect CI\IeI"the y-axis.
PROBLEM SOLVING
UNthe tableto solve.,...,PI'_ 1 1
20. WriIe aneq...im to shawhowto fWld the retail priceof aniten.
11.y-2x-6
Wl\clll'"CoO,. .... ,
... '"
" "
.. "
50 . "
50 '"
Show You Undersulnd Doesa parallelogram have rollllional symmeuy? Explain.
626 Chapter 23 Chapter ReviewfTeSl
Extra Practice
Use grid paper. Usethe coordinates to plot and label each point.
Set A ~1,pp.61G-6131
Use Ihe coordinate plane allhe right for Elercisea 1-7. Write the ordered pair lor each point.
-, ,
•, -, -, , , •
• -, -, • , • c
-, -, c
" 7 -,. .-, " 7 " " " ,
" ,
• 7 •
, -, ". , . " -, •
,_ M ._ 8 Write the leller name 01 each point.
8. W(+3. +5) 11. Z(-S. '1)
Set B ~2.pp.61~151
Make 8 funetion lable tor each 01 the following using 0.4,8,1210' x.
1.y-x+4 2. y" 4,.. 3. y-x-4 4.y-1O-x
Set C ~3,pp.SI6-flllil
Find 4 sela of COOrdinates lor each function. Then graph Ihe functions on grid paper.
1. y-x-6 2. y-x+5 3. y-2x+2 4.y-3x-5
Set D o.-on~.1'P.1m-6251
Use the diagram. Name the coordinates 01 triangle ABCafter the transformations.
1. Translate left 5 units.
2. Reflect over the x-axis.