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# Obj 8- Obj 10c MAC1105

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This 9 page Class Notes was uploaded by Michaela Maynard on Tuesday September 29, 2015. The Class Notes belongs to MAC1105 at Florida State University taught by Pennington LeNoir in Summer 2015. Since its upload, it has received 106 views. For similar materials see College Algebra in Calculus and Pre Calculus at Florida State University.

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Date Created: 09/29/15

M algax6 Objective 8 Linear Equations Obj 8a Slope The slope of the line through 121 31 and 132312 WW m agl Y f m gigglint ofthelinfB and Chfccam Kquotquotl rmquot 39 1 Find the slope of the line through 4 6 and 2 7 4 6 and 4 2 3 2 and 02 4412 mizLZ az tl wari3 71 u 3 1 0 0395 3 me Wnde hated O S Pe N A 0 N y y 91 Cm 0 3 O l L I I I L quotc x x a axD 2K 0 blwlu me NOT VCRhowl Obj 8e Writing the Equation of a line How do we determine the algebraic rule that de nes a particular line the my equation of a line Each line is uniquely determined by Anl 70 313 2b HE and the 26 The equation of the line througBh 131y1 with slope m is given by C I 5 A B 0 b 5 31 he 90 L Stgndgi d FOYW Slo gemlmcCVCCP n On 0V 39 n B C OFOerm 39Hntto bemula Lquot 3 DYe 3 3i P Obj 8e Write an equation of the line that goes through 1 3 and has slope m 2 Express answer in standard form eGrade Instructions lease remember that standard form is AwBy C where I A BCare integers andAgtO W xECigade 94 5 morn A 2 3 m 2 ozx39 quot5 Dgt33 8L2f 5 17 3 0236 27 fj39aw 34 5 I Obj Se Write an equation of the line that goes through 6 3 and has slope m 2 Express answer ijn sfr iiargl ormgb 3 5 1 5X H 3 p 7 21 5 5quot 30 chqradeC 3 03 7 quotTKquotltquot 5 7 R 3930 W 7 Maeaw amp m SW Obj 8e Write an equation of the line that goes through 3 9 and 12 1 Express answer in slopeintercept form eGrade Instructions Enter only the right hand side of the expressmnm Use W proper or im roper fractions or exact decimals mixed fractions and decimal approximations are t m l4 22 3 3 quotSL LD Wquot J 15 3 3 33 K 2 x 2 e y 306 3quot quot26 w 7 92 Web ry3 5L7 jgn1 9 w3gtq 3 Obj 8e Write an equation of the line that goes through 0 b and has slope m Express answer in slopeintercept form gaunt aawx rb nygayxdavd Formx mg 4 0 1 b Obj 8C Identify the slope of a line Write in slopeintercept 01m Unless special cases of vertical or horizontal line see below Find the slope of the line 2m y 5 Ryn 5 3 M Qx Obj 8b Graph of Linear Equation Plan of Attack Just nd the It isn t necessary to put in slopeintercept form 28 3F 3 WV VCep39bS V X Obj 8b Which of the following most closely resembles the graph of 11 3y 2 36 54 x c O y 7 Ty V 3 a l0 m xv xy 3 OK 1 33 30 392 a3 Obj 8d Summary of facts for Vertical and Horizontal lines 3 3quot quot Xi l2 Horizontal line has equation 5Q has slope m 3 2 except for xaxis has no I nth Vertical line has equation L 5 C has slope Ling C nqlexcept for yaxis has no 5 quot ht Obj 80 Find the slope of the line cum 5ch 9m alrcaouj solvch 13w V Yb lme and med suppCV ho zomtal lint Mco Obj 8d Write an equation of the line that goes through 2 4 that has unde ned slope 3 9 quot W OL V I undclhned N COW E plug vvcr ocm m quotAundc med x c c Obj 8d Write an equation of the line that goes through 2 4 that has no x intercepts hovx conwl a a w Obj 8d Write an equation of the line that goes through 5 1 and 5 4 V fttwl l C 29 Obj 8f Using slope of parallel or perpendicular lines to write an equation of a line Plan of Attack For nonvertical lines M Parallel lines have the a W C 3 M76 Perpendicular lines have slopes whose IUYQjUC b 5 l f CCAVYocal 3 5 3 For example if a line has slope m 3 then a line that s perpendicular has slope W quot 5 For vertical lines we must use geometry Two vertical lines are parallel they never intersect A vertical line and a horizontal are perpendicular they intersect in a 90 angle Sam C OIVH Obj 8f Write an equation of the line that goes through 2 5 that slperpendicular to the line 811 3y 7J The multiple choices are 311 standardform ABC in egers and Agt 0 yawnxh m 83 6345746043 Mfay39 59 is 2 83quot sum 33 gw tour lmC 3 1 940 393 4 t t 83an 73 3 339 V 39 39 V V Rowem 8 lor OH 3 m 3il zwnce m 373 Woof V VH3 lime Obj 8f Write an equation of the line that goes through 4 3 and islparallel to y 2amp1 g39 9 W Mn quot we 30m stoPe 3 3 3L LAB Mun b 9331V gt L 5 4 cho ce39 5gi5x H Obj 8f Write an equation of the line that goes through 1 5 that s parallel to the line 3 3 m L f39 0 quot quot5 L 3 when 3 fo t 30WJG MR x our me 3 vu mcal Obj 8e Linear Applications Writing the equation of a line c My fb Plan of Attack 9 When written in slope intercept form we say 14 F The express sentence tells you how to set up the ordered pairs You cannot lC OY C H b 30 419 As one descel dscgnto the ocean pressure increases linearly The pressure is 15 pounds per square 39 inch on the surface and 30 pounds per square inch 33 feet below the surface Ex re s the ressure p in pounds per square inch in terms of the de th 1 in feet below the surface nter only the right hand side of the expressi Use con rge e Use proper or improper fractions no mixed fractions or exact decimals Do not give decimal approximations k pr s P In terms 04 d d A 5 mgw 35 T I 939 WW b t V n xomered sawi39fdirl 3 5 OMS VRem mlocr to EmmaquotO 173gtquotquotjquotM P use COUCH variable 3330 Blue whales weigh approximately 2 tons when newborn Young whales are nursed for 9 months and by the time of weaning they often weigh 25 tons Let 0 denote the weight of the whale in tons and let 9 be the aggof the whaleln months 39If the welght 1s llnearly related to the age express to 39 in terms of a Same onlme cautlons shown in rst example azz Ehtfir o l K 65 W I q a R l n Ext 3 w m ttrm of a ght 5m w MG H0 51539 23 WV 3971quot OYdQY Cd mixslow 390 Gnvcw o 1 6 lg39mt 6135 The volume v in cubic centimeters of a gas varies linearly with temperature t in degrees Celsius At a temperature of 12 C a gas occupies a volume of 2800m3 When warmed to 66 C the gas occupies a volume of 361cm3 Express 12 in terms of 25 Same eGrade cautions shown in rst C militia v m bcrms at a WIZ 5 OV form V Vi W T quot Mi b 39 V V BXO Jo 2 m 39 go dcrco Vows 1tv euch n 830 0 WA Jr WEBB w kMethod 31mm me lag fm 2quot i v 331 Ho 4 2X0 Vagakb The volume v in cubic centimeters of a gas varies with temperature39t391n degrees Celsius At a temperature of 12 C a gas occupies a volume of 28007123 When warmed to 66 C the gas occupies a volume of 36lcm3 Express t in terms of 22 Same eGrade cautions shown in rst example 1 Lab 439 3 3547633 t39 m terms 05 V Mawass 3 te MVHo t t w V wQ vtlaygfwato aordered WWSZCVJ Q 31 20430 Guvcwaltgoua 39100 6 3 A peanut farmer nds that at an average cost of per bushel 300 bushels can be produced 1200 bushels can be produced at an average of 2 per bushel Assuming that the cost per bushel c and the number of bushels n are linearly related Express c in terms of n Emwess c m terms 0 n m 3quot a quotquotquot 1quot quotquotquotquot C nmrx b aco39mao 700 Ovscme 0539YCgt 39le Cmvcn 3005 6300 Obj 9 CenterRadius Form of the Equation of a Circle centthM 35 Don Fovmma y Mg foamy r thgrby Centtw adm Forge 0 CrC 39 M43 4493 hla a MM3 MfMDYIZc Identify the center and radius x 32y 2225 m22y1r5 x2yl324 3a Ll quot o quot centerz xm 433 3 74 if a T A f K rad lb Jig quot b Cev icK h K 5 Qf39b 3 rodxus J75 Clem O 6 quotl r 3 32 Qattllf Objective 10 Functions A function is an algebraic rule or a correspondence between sets that associates each element x from one set with a M I Mag C element y of another set The set of x s is the 6W0 h The set of y s is the 0 31 gt O Y 9 Obj 10a Identify a Function from graph or set of ogits 3 Genbf F 0 9 Consider x2y24 V L Oa 9 0 3 The graph of a function must pass the VCKU C0 W f t S S an amp Ont ver mm mC v SCCt3 hWC O Ph V at MOST DYVC ixm t t 6 the I 04 80 3 tha h 0 O 39R W mon 3 311 M70 Which represent the graph of a function Read carefully sometimes we ask Which do not represent the graph of a function mks ml y y 5 bvvxe one 1 3 939 NO Q a 8m rms 3 a graph ngh of 0 hm cam 1 w won 4 Which are functions OS 0 n O D RJWCUOY 11 2 3a 2 5v t x 4 308160 all x WM 3 W63 must Show LAP cmmgl 17 2 139 21 13 Lquot I NO a Pumdnom Obj 10b Function Notation Evaluate a function Instead of writing y 3132 5x 8 we now write f 3x2 551 8 faPL Instead of saying let x 2 nd y we now write f2 quotl3 0 2 a 52335a2r ao8 no f ammem 33 awlyt 0 domain vm ocm m quot 392 Punctxons Find each of the following for phe functions given below dfnm Cbn StanL fa 3m2 5x8 927 23 5132 hx 3 5xl mc 3 nc 2 4 quot46 j 5 B a a glt 1gt 3 47 M 3 3a 0 05 20 quot 33 2 3x av5xfa 4 quot 0S 39 3quot z a 3X2 HLHgt 5 733 8wh h sand5 0th x530 3 a0 kindaquot 3 a a Olt6 ICE L I 3 I p d g h 3 3 50 33 quot 1 Bo gs lsr i 2 I h13 b0 539 339 K Hquot 6 5 z z 3 W as 13M m 3 L3 Rwh39h 2151 E mlt3gt 3 M5 5 nlt 3gt a no 2 m2a 2a mxh K39r n n2a a nah 2 END OF Tia 51 1 MATERIAL Obj 100 Domain and Range Give Domain and Range from the graph of a function 339 p s rme v haVHY 33935 3 2 Q 3 m E CD D C J D doe9W3 R i 00gt R3ij 00 D0m0mw vau 3oo4 ch v c 00K bottom4V0 ann vmuteS 34 More Obj 100 Give Domain only from the function rule We re being asked for the 11 set of real numbers that can be substituted in for g What prevents a value from being plugged in for a When might the domain not be all real numbers There are only TWO situations that limit restrict the values that can be used for 13 O NDW SWY 0 wwngatatwc aw twa Q lAnCUDY we dogma vwa exther 0 meme then 0600 Give the Domain fr 3x7 5x4 xg 933 2 3 51 I 17 hc 31 1 06003 DIGOOJND D139 0J Dgt ea53 gt my be pas 36 7 go 31 Z quotI 00gt 7 1 3 y 3

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