Kumathematika, ukuthambekela noma ukuhleleka komugqa inombolo echaza kokubili isiqondiso nokushuba komugqa (ikhala iWikipedia). Ibalwa ngokuthola isilinganiso soshintsho ku-y-coordinate kuya kushintsho ku-x-coordinate phakathi kwamaphoyinti amabili ahlukene emugqeni.

Isibonelo, uma unamaphuzu amabili emugqeni, (1,2) kanye no-(3,4), ukuthambekela komugqa phakathi kwawo ngu-(4-2)/(3-1) = 2/2 = 1. Sizofika kulokhu maduze nje.

I-Slope ingumqondo obalulekile kwizibalo futhi inezinhlelo zokusebenza eziningi zomhlaba wangempela. Ngokwesibonelo, ingasetshenziswa ukubala isivinini sento, izinga lokushintsha komsebenzi, noma umqansa wegquma.

Emhlabeni wangempela, i-slope isetshenziswa emikhakheni ehlukahlukene efana ne-geography, ubunjiniyela bomphakathi, i-architecture, kanye ne-physics. Ku-geography, i-slope isetshenziselwa ukuchaza ukukhuphuka komhlabathi. Isetshenziselwa ukukhombisa ukugeleza kwamanzi, ukubonisa indawo yokuhlala, ukuhlukanisa inhlabathi, ukuhlola amandla okuthuthuka, kanye nesibonelo sengozi yomlilo wequbula.

Kwezobunjiniyela bomphakathi, i-slope isetshenziselwa ukuklama imigwaqo, amabhuloho, nezinye izakhiwo. Isetshenziselwa ukunquma indlela engcono kakhulu yokuqedela iphrojekthi futhi kwakhiwe izindawo zokuphambuka zezihlalo zabakhubazekile, imigwaqo, nezitebhisi.

Ekwakhiweni kwezakhiwo, i-slope isetshenziselwa ukuklama izakhiwo nezakhiwo ezinzile futhi eziphephile. Ku-physics, i-slope isetshenziselwa ukuchaza isivinini sento ngokuhamba kwesikhathi.

Ngiqonde ukukhuluma ngokubaluleka...

Imiqondo Eyisisekelo Ye-Slope

I-slope ibalwa njengesilinganiso soshintsho oluma mpo (ukukhuphuka) ukuya ekushintsheni okuvundlile (gijima) phakathi kwamaphoyinti amabili emugqeni.

Ifomula yemithambeka ichazwa ngokuthi m = (y2 – y1) / (x2 – x1).

Kufomula engenhla, kunamaphuzu amabili, manje iphuzu ngalinye linazo zombili ivalve engu-y ehambisanayo kanye nenani lika-x. Ukudidiyelwa kwephuzu1 ngu (x1, y1) futhi lokho kwephuzu2 ngu (x2, y2) njengoba kuboniswe emfanekisweni ongenhla.

Kunezinhlobo ezine zemithambeka: iphozithivu, inegethivu, uziro, futhi engachaziwe.

I-slope ephozithivu ibonisa ukuthi umugqa uyakhula ukusuka kwesokunxele ukuya kwesokudla, kuyilapho umthambeka ongemuhle ubonisa ukuthi umugqa uyancipha ukusuka kwesokunxele ukuya kwesokudla.

Imithambeka enguziro ibonisa ukuthi umugqa uvundlile, kuyilapho umthambeka ongachazwanga ubonisa ukuthi umugqa umile.

Umdwebo ongezansi ubonisa izinhlobo ezahlukene zemithambeka:

Ukubala iSlope: Isinyathelo ngesinyathelo Umhlahlandlela

Kulesi sigaba, sizobe sidlula kumhlahlandlela wesinyathelo ngesinyathelo sendlela yokubala umthamo

Ngezansi umhlahlandlela wesinyathelo ngesinyathelo sendlela yokubala umthambeka:

1. Thola amaphuzu amabili emgqeni.
2. Khetha iphuzu elilodwa libe (x1, y1) bese elinye libe (x2, y2).
3. Thola ushintsho oluma mpo (ukhuphuke) ngokukhipha izixhumanisi zika-y zamaphuzu amabili.
4. Thola ushintsho oluvundlile (gijima) ngokukhipha izixhumanisi ezingu-x zamaphuzu amabili.
5. Hlukanisa ushintsho oluma mpo ngoshintsho oluvundlile (khuphuka phezu kokugijima) ukuze uthole umthambeka.

Nasi isibonelo sokukhombisa izinyathelo ezingenhla:

Ake sithi sinamaphuzu amabili emgqeni, (1, 2) kanye no-(3, 6).

Singabala ukuthambeka komugqa kanje:

1. Khomba amaphuzu amabili emugqeni: (1, 2) kanye (3, 6).
2. Khetha iphuzu elilodwa ukuthi libe (x1, y1) bese elinye libe (x2, y2): Ake sikhethe (1, 2) njengo (x1, y1) kanye (3, 6) njengo (x2, y2).
3. Thola ukuguqulwa okuqondile (ukukhuphuka) ngokukhipha izixhumanisi zika-y zamaphuzu amabili: 6 - 2 = 4.
4. Thola uguquko oluvundlile (gijima) ngokukhipha izixhumanisi ezingu-x zamaphuzu amabili: 3 - 1 = 2.
5. Hlukanisa ushintsho oluma mpo ngoshintsho oluvundlile (khuphuka phezu kokugijima) ukuze uthole umthambeka: 4/2 = 2.

Ngakho-ke, i-Slope ingu-2. I.e umthambeka omuhle

Nasi esinye isibonelo ukukhombisa lezi zinyathelo ezingenhla:

Ake sithi sinamaphuzu amabili emgqeni, (3, 7) kanye no-(1, 10).

Singabala ukuthambeka komugqa kanje:

1. Khomba amaphuzu amabili emugqeni: (3, 7) kanye (1, 10).
2. Khetha iphuzu elilodwa ukuthi libe (x1, y1) bese elinye libe (x2, y2): Ake sikhethe (3, 7) njengo (x1, y1) kanye (1, 10) njengo (x2, y2).
3. Thola ukuguqulwa okuqondile (ukukhuphuka) ngokukhipha izixhumanisi zika-y zamaphuzu amabili: 10 - 7 = 3.
4. Thola uguquko oluvundlile (gijima) ngokukhipha izixhumanisi ezingu-x zamaphuzu amabili: 1 – 3 = -2.
5. Hlukanisa ushintsho oluma mpo ngoshintsho oluvundlile (khuphuka phezu kokugijima) ukuze uthole umthambeka: 3 / -2 = -1.5.

Ngakho-ke, i-Slope ingu-1.5. I.e. umthambeka omubi.

Nawa amanye amathiphu okugwema amaphutha avamile lapho ubala umthambeka:

1. Qonda umqondo wokuthambeka: I-Slope ibalwa njengesilinganiso soshintsho ku-y kuya kushintsho ku-x. I-slope ephozithivu ikhombisa ithrendi eya phezulu, kuyilapho i-slope eyinegethivu ikhombisa ukwehla.
2. Hlola kabili izibalo zakho: Izibalo ze-slope zingaba nzima, ngakho-ke kubalulekile ukuthi uhlole kabili umsebenzi wakho. Qiniseka ukuthi unamanani alungile oshintsho luka-y kanye noshintsho luka-x, nokuthi uwahlukanise ngendlela efanele.
3. Yenza ukusetshenziswa I-Slope Calculator: Ukwenza ukusetshenziswa umshini wokubala womthambeka izonciphisa kakhulu amaphutha.

Nakhu a I-Slope Calculator ongayisebenzisa ukuze ubale umthambeka noma i-gradient phakathi kwamaphoyinti amabili ohlelweni lwe-Cartesian coordinate. 

Okufanele ukwenze uma usebenzisa lesi sibali semithambeka ukufaka inani elingu-x1, x2, y1, y2. 

Isibali sizobala ngokuzenzakalelayo umthambeka, i-equation yomugqa, ukuphakama, ukugijima, ibanga phakathi kwamaphoyinti amabili, nokunye okuningi, akudingekile ukuthi ucwayize kabili.

Umthambeka kuJiyomethri

Njengoba sishilo ekuqaleni, iSlope isilinganiso sokukhuphuka komugqa.

Konxantathu, ukuthambeka komugqa kungasetshenziswa ukubala i-engeli phakathi komugqa ne-eksisi ka-x.

Umthamo womugqa ungasetshenziswa futhi ukunquma ukuthi imigqa emibili iyahambisana yini noma i-perpendicular. Imigqa emibili iyahambisana uma inomthambeka ofanayo, futhi i-perpendicular uma amamithambeka ayo enokuphindaphindana okungekuhle komunye nomunye.

Izicelo Zomhlaba Wangempela

• Ezokwakha kanye Nezokwakha: Izibalo zemithambeka zisetshenziswa ekuklameni amarempu, izitebhisi, nophahla. I-pitch yophahla, isibonelo, inquma ukuthi ingakanani impahla ezosetshenziselwa ukwakha uphahla kanye nokusebenza kophahla.

• I-physics: Izibalo zemithambeka zisetshenziswa emidwebeni enyakazayo nenamandla. Isibonelo, ukuthambeka kwegrafu yesikhathi sokuma kunikeza isivinini sento.
• Ezomnotho: Izibalo zemithambeka zisetshenziselwa ukuqonda amathrendi. Isibonelo, ukuthambeka kwejika lokufuna kunikeza inani inani elifuna izinguquko mayelana nenani.

Izibonelo Ezisebenzisanayo Nokuzivocavoca

Lesi sigaba sinikeza isethi yezibonelo ezisebenzisanayo nezivivinyo ukusiza ukuqinisa ukuqonda kwakho izibalo zemithambeka.

Inkinga 1:

Cabangela amaphuzu amabili endizeni exhumanisayo: ( A(2, 5) ) kanye ( B(4, 9) ). Bala ukuthambeka komugqa odlula kulawa maphuzu usebenzisa ifomula yemithambeka.

Isixazululo:

m = (9 – 5) / (4 – 2) = (4)/(2) = 2

Inkinga 2:

Uma unikezwe amaphuzu amabili ( C(3, 8)) kanye ( D(7, 2) ), bala ukuthambeka komugqa odlula kulawa maphuzu usebenzisa ifomula yemithambeka.

Isixazululo:

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

Izimo Zempilo Yangempela

Isimo 1: I-Ramp Design

Zibone ngeso lengqondo ungumdwebi wezakhiwo onikezwe umsebenzi wokudizayina irempu yesihlalo esinamasondo sokungena ebhilidini. Sebenzisa izibalo zemithambeka ukuze unqume ukuthambekela okuphelele kokufinyeleleka kuyilapho unamathela ezindinganisweni zokuphepha.

Isimo 2: Amathrendi Ezomnotho

Njengomhlaziyi wezezimali, hlaziya isethi yamaphoyinti edatha yezomnotho ngokuhamba kwesikhathi futhi ubale umthamo ukuze uhlonze amathrendi. Ngabe lolu lwazi lungabaluleka kanjani ekwenzeni izibikezelo ezinolwazi?

Manje, ibhola ngelakho ongalidubula, Yabelana ngezisombululo zakho noma izindlela osebenzise ngazo izibalo zomthambeka empilweni yakho. Kungakhathaliseki ukuthi ukuklama kabusha ingadi yakho, noma ukuphuza ingilazi yamanzi.

Zizwe ukhululekile ukuthumela izixazululo zakho noma wabelane ngolwazi lwakho.

Isiphetho

Sifike ekugcineni kwalesi sihloko, ake siphinde sifunde amaphuzu abalulekile abhalwe kulesi sihloko

Amaphuzu ayisihluthulelo:

• I-Slope ikala ukushuba komugqa futhi ibalulekile kwizibalo nasezinhlelweni ezihlukahlukene zomhlaba wangempela.
• Ifomula yemithambeka ( m = {y2 – y1} / {x2 – x1} )
• Izinhlobo ezi-4 zeSlope yilezi; Imithambeka emihle, engemihle, eyiziro, kanye nengachazwanga futhi ngayinye idlulisela ulwazi oluhlukile mayelana nezici zomugqa.
• Emhlabeni wangempela, i-slope isetshenziswa emikhakheni ehlukahlukene efana ne-geography, ubunjiniyela bomphakathi, i-architecture, kanye ne-physics.