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Graad 9


Grafiese voorstellings




Module 15

Vergelyking van ‘n reguitlyn-grafiek vanuit ‘n diagram


Om die vergelyking van ’n reguitlyn-grafiek vanuit ’n diagram te bepaal

[LU 2.5]

  1. As ons die waardes van m en c kan uitwerk, kan ons hierdie waardes direk in die algemene vergelyking y = mc + c instel om sodoende die bepalende vergelyking van die lyn te verkry. Hier is ’n voorbeeld uit die diagram.

Dis maklik om c te bepaal, aangesien dit dié waarde (positief of negatief) is waar die lyn die y-as sny. Substitueer hierdie waarde (dis –1) vir c.

Nou is die vergelyking y = mх – 1. Om die gradiënt (die waarde van m) te bepaal, konstrueer ons die reghoekige driehoek tussen twee geskikte punte op die lyn, waar die grafiek presies deur twee hoekpunte van die grafiekpapier gaan.

  • Ons weet m is ’n breuk, t.w..
verandering in vertikale afstand
verandering in horisontale afstand
  • Ons lees die aantal eenhede van die hoogte en van die basis van die driehoek om die teller en die noemer onderskeidelik te kry.
  • Ons bepaal ook die teken van m deur te kyk of die lyn opwaarts of afwaarts na regs loop.
  • Nou het ons: m = 4 6 = 2 3 size 12{ size 11{m```=``` - { { size 8{4} } over { size 8{6} } } ```=``` - { { size 8{2} } over { size 8{3} } } }} {} (onthou om die breuk te vereenvoudig).
  • Hierdie waarde vervang nou vir m in die vergelyking: y = 2 3 x 1 size 12{ size 11{y```=``` - ``` { { size 8{2} } over { size 8{3} } } x``` - ```1}} {} . Dit is die bepalende vergelyking van die lyn.
  • Gebruik nou hierdie metode om die bepalende vergelykings van die agt grafieke in die eerste twee diagramme van die vorige deel uit te werk.

2 Wat van horisontale en vertikale lyne? Hulle is die maklikste!

  • ’n Horisontale lyn het die algemene vergelyking y = c . Ons moet ’n waarde vind om c mee te vervang. Hierdie waarde word van die grafiek afgelees – die y -afsnit! Substitueer vir х
  • en daar het jy die bepalende vergelyking.
  • Die algemene vergelyking van ’n vertikale lyn is х = k . Bepaal k deur van die grafiek te lees waar die lyn die х –as sny, en substitueer hierdie waarde vir k . Dit gee ons die bepalende vergelyking.
  • Bepaal nou die vergelykings van die vier lyne in die laaste diagram van die vorige deel.

Die antwoorde is: y = 1 en y = –1,5 is die horisontale lyne, en х = –1 en х = –2,5 is die twee vertikale lyne.

  1. Hier is nou ’n mengsel lyne om jou vaardighede mee te toets!

4 Het jy opgelet dat die gradiënte ( m ) van lyne G en H dieselfde is? Waarom?


Om die gradiënt van ’n reguit lyn vanuit twee gegewe punte te bereken

[LU 2.5]

  • As die koördinate van twee punte op ’n sekere reguit lyn bekend is, is dit maklik om die lyn te trek, soos jy weet. Ons kan ook die gradiënt aflei uit ’n skets. Maar dit is nie nodig om ’n skets te hê om die gradiënt te bepaal nie.
  • Hier is ’n voorbeeld: Die punte (3 ; –1) en (4 ; 2) lê op ’n sekere reguit lyn.
  • Eers bepaal ons die vertikale afstand tussen die punte deur die tweede punt se y -koördinaat van die eerste punt se y -koördinaat af te trek. Dit gee die teller van die gradiënt.
  • Dan bereken ons die horisontale afstand tussen die twee punte deur die tweede punt se х -koördinaat van die eerste punt se х -koördinaat af te trek. Nou het ons die noemer van die gradiënt.
  • Dus is die gradiënt: m = vertikale afstand horisontale afstand = 1 2 3 4 = 3 1 = 3 size 12{ size 11{m``=`` { { size 11{"vertikale"``"afstand"}} over { size 11{"horisontale"```"afstand"}} } ``=`` { { size 11{ - 1` - `2}} over { size 11{3 - 4}} } ``=`` { { size 11{ - 3}} over { size 11{ - 1}} } ``=`} size 13{`}3} {}

Questions & Answers

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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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