Kwimathematika, ukuthambeka okanye ukuthambeka komgca linani elichaza zombini icala kunye nobunzulu bomgca (iyakhala iWikipedia). Ibalwa ngokufumana umlinganiselo wotshintsho kwi-y-coordinate kwinguqu kwi-x-coordinate phakathi kwamanqaku amabini ahlukeneyo kumgca.

Umzekelo, ukuba unamanqaku amabini kumgca, (1,2) kunye (3,4), i-slope yomgca phakathi kwabo (4-2) / (3-1) = 2/2 = 1. Siza kufika kule nto ngokukhawuleza ngokwaneleyo.

I-Slope yingcamango ebalulekileyo kwimathematika kwaye inezicelo ezininzi zehlabathi lokwenene. Umzekelo, inokusetyenziswa ukubala isantya sento, isantya sokutshintsha komsebenzi, okanye umnqantsa wenduli.

Kwihlabathi lokwenyani, ithambeka lisetyenziswa kwiinkalo ezahlukeneyo ezifana nejografi, ubunjineli boluntu, ulwakhiwo, kunye nefiziksi. Kwijografi, ithambeka lisetyenziswa ukuchaza umnqantsa womphezulu womhlaba. Isetyenziselwa ukwenza umfuziselo wokubaleka komhlaba, ukubonakalisa indawo yokuhlala, ukwahlula umhlaba, ukuhlola okunokwenzeka kophuhliso, kunye nomzekelo womngcipheko womlilo wasendle.

Kubunjineli boluntu, ithambeka lisetyenziselwa ukuyila iindlela, iibhulorho kunye nezinye izakhiwo. Isetyenziselwa ukumisela eyona ndlela ilungileyo yokugqiba iprojekthi kunye nokwakha iirempu zesitulo esinamavili, iindlela, kunye nezinyuko.

Kwi-architecture, i-slope isetyenziselwa ukuyila izakhiwo kunye nezakhiwo ezizinzileyo nezikhuselekileyo. Kwifiziksi, ithambeka lisetyenziswa ukuchaza isantya sento ngokuhamba kwexesha.

Ndithetha ngokubaluleka...

Concepts Basic of Slope

I-Slope ibalwa njengomlinganiselo wotshintsho oluthe nkqo (ukunyuka) ukuya kutshintsho oluthe tye (ukuqhuba) phakathi kwamanqaku amabini kumgca.

Ifomula yethambeka ichazwa njenge m = (y2 – y1) / (x2 – x1).

Kwifomula engentla, kukho amanqaku amabini, ngoku inqaku ngalinye linazo zombini ivalve ehambelana no-y kunye nexabiso lika-x. Ulungelelwaniso lwenqaku1 ngu (x1, y1) kunye nelo nqaku2 ngu (x2, y2) njengoko kubonisiwe kulo mfanekiso ungasentla.

Kukho iindidi ezine zamathambeka: i-positive, negative, zero, kunye ne-undefined.

I-slope e-positive ibonisa ukuba umgca uyanda ukusuka ekhohlo ukuya ekunene, ngelixa i-slope e-negative ibonisa ukuba umgca uyancipha ukusuka ekhohlo ukuya ekunene.

Ithambeka elingu-zero libonisa ukuba umgca uthe tye, ngelixa i-slope engachazwanga ibonisa ukuba umgca ume nkqo.

Lo mzobo ungezantsi ubonisa iindidi ezahlukeneyo zamathambeka:

Ukubala ukuthambeka: ISikhokelo seNyathelo ngeNyathelo

Kweli candelo, siza kudlula kwisikhokelo senyathelo nenyathelo malunga nokubala ukuthambeka

Apha ngezantsi sisikhokelo senyathelo nenyathelo malunga nokubala ukuthambeka:

1. Chonga amanqaku amabini emgceni.
2. Khetha inqaku elinye libe (x1, y1) kwaye elinye libe ngu (x2, y2).
3. Fumana utshintsho oluthe nkqo (ukunyuka) ngokuthabatha i-y-coordinates yamanqaku amabini.
4. Fumana utshintsho oluthe tye (ukuqhuba) ngokuthabatha u-x-ulungelelaniso lwamanqaku amabini.
5. Yahlula uguquko oluthe nkqo ngotshintsho oluthe tye (ukuphakama phezu kokubaleka) ukufumana ithambeka.

Nanku umzekelo obonisa la manyathelo angasentla:

Masithi sinamanqaku amabini emgceni, (1, 2) no-(3, 6).

Sinokubala ukuthambeka komgca ngolu hlobo lulandelayo:

1. Chonga amanqaku amabini emgceni: (1, 2) kunye (3, 6).
2. Khetha inqaku elinye libe (x1, y1) kwaye elinye libe ngu (x2, y2): Masikhethe (1, 2) njengo (x1, y1) no (3, 6) njengo (x2, y2).
3. Fumana utshintsho oluthe nkqo (ukuphakama) ngokuthabatha u-y-ulungelelwaniso lwamanqaku amabini: 6 - 2 = 4.
4. Fumana inguqu ethe tye (baleka) ngokuthabatha ux-ulungelelwaniso lwamanqaku amabini: 3 - 1 = 2.
5. Yahlula inguqu ethe nkqo ngotshintsho oluthe tye (ukuphakama phezu kokubaleka) ukufumana ithambeka: 4 / 2 = 2.

Ngoko ke, i-Slope yi-2. I.e i-slope e-positive

Nanku omnye umzekelo obonisa la manyathelo angasentla:

Masithi sinamanqaku amabini emgceni, (3, 7) no-(1, 10).

Sinokubala ukuthambeka komgca ngolu hlobo lulandelayo:

1. Chonga amanqaku amabini emgceni: (3, 7) kunye (1, 10).
2. Khetha inqaku elinye libe (x1, y1) kwaye elinye libe ngu (x2, y2): Masikhethe (3, 7) njengo (x1, y1) no (1, 10) njengo (x2, y2).
3. Fumana utshintsho oluthe nkqo (ukuphakama) ngokuthabatha u-y-ulungelelwaniso lwamanqaku amabini: 10 - 7 = 3.
4. Fumana inguqu ethe tye (baleka) ngokuthabatha ux-ulungelelwaniso lwamanqaku amabini: 1 – 3 = -2.
5. Yahlula inguqu ethe nkqo ngotshintsho oluthe tye (ukuphakama phezu kokubaleka) ukufumana ithambeka: 3 / -2 = -1.5.

Ngoko ke, i-Slope yi-1.5. I.e. ithambeka elibi.

Nanga amanye amacebiso okuphepha iimpazamo eziqhelekileyo xa ubala ukuthambeka:

1. Qonda ingqikelelo yethambeka: Ukuthambeka kubalwa njengomlinganiselo wotshintsho ku-y kutshintsho ku-x. Ithambeka elivumayo libonisa ukuthambekela okuya phezulu, ngelixa ithambeka elibi libonisa ukuhla.
2. Jonga kwakhona izibalo zakho: Ubalo lwe-slope lunokuba lukhohlisayo, ngoko ke kubalulekile ukuphinda uhlolisise umsebenzi wakho. Qinisekisa ukuba unamaxabiso achanekileyo otshintsho ku y kunye notshintsho ku x, kwaye uzahlule ngokuchanekileyo.
3. Sebenzisa I-Slope Calculator: Sebenzisa i- ithambeka lokubala iya kunciphisa kakhulu iimpazamo.

Nantsi i I-Slope Calculator onokuzisebenzisa ukubala ithambeka okanye ithambeka phakathi kwamanqaku amabini kwinkqubo yolungelelwaniso lweCartesian. 

Into ekufuneka uyenzile xa usebenzisa le calculator yethambeka kukufaka ixabiso lika x1, x2, y1, y2. 

I-calculator iya kubala ngokuzenzekelayo i-slope, i-equation yomgca, ukunyuka, ukugijima, umgama phakathi kwamanqaku amabini, kunye nokunye okuninzi, akufanele uqhwanyaze kabini.

Ukuthambeka kwijiyometri

Njengoko besesitshilo ngaphambili, i-Slope ngumlinganiselo womnqantsa womgca.

Koonxantathu, ukuthambeka komgca kungasetyenziswa ukubala i-engile phakathi komgca kunye nomgca ongu-x.

I-slope yomgca ingasetyenziselwa ukujonga ukuba imigca emibini ihambelana okanye i-perpendicular. Imigca emibini iyahambelana ukuba inethambeka elifanayo, kwaye i-perpendicular ukuba i-slopes yabo i-reciprocals negative enye kwenye.

Real-World Application

• Ulwakhiwo kunye neZakhiwo: Izibalo zokuthambeka zisetyenziswa ekuyileni iirempu, izinyuko, nophahla. Umgangatho wophahla, umzekelo, umisela ukuba zininzi izinto eziza kusetyenziswa ukwakha uphahla kunye nokusebenza kophahla.

• YeFizikiki: Ubalo lwe-slope lusetyenziswa kwimizobo eshukumayo kunye nokunyanzeliswa. Umzekelo, i-slope ye-position-time graph inika isantya sento.
• Economics: Izibalo zokuthambeka zisetyenziselwa ukuqonda iintsingiselo. Umzekelo, i-slope ye-curve yemfuno inika ireyithi apho ubungakanani obufuna utshintsho ngokumalunga nexabiso.

Imizekelo eSebenzayo kunye neMithambo

Eli candelo libonelela ngeseti yemizekelo esebenzisanayo kunye nemithambo ukunceda ukuqinisa ukuqonda kwakho izibalo zemithambeka.

Ingxaki 1:

Qwalasela iingongoma ezimbini kwinqwelo-moya elungelelanisiweyo: ( A(2, 5) ) no ( B(4, 9) ). Bala i-slope yomgca odlula kula manqaku usebenzisa i-slope formula.

isisombululo:

m = (9 – 5) / (4 – 2) = (4)/(2) = 2

Ingxaki 2:

Unikwe amanqaku amabini ( C (3, 8) ) kunye ( D (7, 2) ), bala ukuthambeka komgca odlula kula manqaku usebenzisa ifomyula yethambeka.

isisombululo:

m = (2 – 8) / (7 – 3) = (-6)/(4) = -1.5

Iimeko zoBomi bokwenyani

Inkcazo 1: Uyilo lweRamp

Khawufane ucinge ukuba ungumyili wezakhiwo onikwe umsebenzi wokuyila indlela yesitulo esinamavili sokungena kwisakhiwo. Sebenzisa izibalo zemithambeka ukumisela elona thambeka lifanelekileyo lokufikeleleka ngelixa ubambelela kwimigangatho yokhuseleko.

Inkcazo 2: Iindlela zoqoqosho

Njengomhlalutyi wezezimali, hlalutya isethi yamanqaku edatha yezoqoqosho ngexesha kwaye ubale ukuthambeka ukuchonga iindlela. Ingaba olu lwazi lunokuba luncedo njani ekwenzeni uqikelelo olunolwazi?

Ngoku, ibhola yeyakho yokudubula, Yabelana ngezisombululo zakho okanye iindlela oye wasebenzisa ngayo izibalo zokuthambeka ebomini bakho. Nokuba kukuyila kwakhona igadi yakho, okanye ukusela iglasi yamanzi.

Zive ukhululekile ukuthumela izisombululo zakho okanye wabelane ngamava akho.

isiphelo

Sifike ekupheleni kweli nqaku, makhe siphinde sibuyele iingongoma eziphambili ezibhalwe kweli nqaku

Amaphuzu aphambili:

• I-Slope ilinganisa ubunzulu bomgca kwaye ibalulekile kwimathematika nakwiinkqubo ezahlukeneyo zehlabathi lokwenyani.
• Ifomula yethambeka ( m = {y2 – y1} / {x2 – x1} )
• Iindidi ezi-4 zamaThambeka zezi; Ithambeka elilungileyo, elibi, elinguziro, kunye elingachazwanga kwaye ngalinye lidlulisela ulwazi olulodwa malunga neempawu zomgca.
• Kwihlabathi lokwenyani, ithambeka lisetyenziswa kwiinkalo ezahlukeneyo ezifana nejografi, ubunjineli boluntu, ulwakhiwo, kunye nefiziksi.