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إذا ﻛﺎن ﻣﺗﺻﻔﺣك ﻻ ﯾﺗﺑﻊ اﻟراﺑط ﺗﻠﻘﺎﺋًﯾﺎ ﻓﻲ ﻏﺿون 3ﺛواٍن ،ﻓﺎﻧﻘر ﻋﻠﻰ اﻟراﺑط !أدﻧﺎه
https://PaperHelp.space <<<اﻧﻘر ھﻧﺎ>>> ھﻮ ﻣﯿﻞ اﻟﺨﻂ ﻧﻔﺲ mﺣﯿﺚ ان y = mx + bرﺑﻤﺎ اﻧﺘﻢ ﺗﻌﺮﻓﻮن ان اي ﻣﻌﺎدﻟﺔ ﺧﻄﯿﺔ ﯾﻤﻜﻦ ان ﺗﻜﺘﺐ ﺑﺼﻮرة Rockland Community College . واﻋﺘﻘﺪ اﻧﮫ ﻣﻦ اﻟﺴﮭﻞ yﺗﻘﺎطﻊ yھﻮ ﺗﻘﺎطﻊ bاﻟﻤﯿﻞ اﻟﺬي ﻛﻨﺎ ﻧﺘﻌﺎﻣﻞ ﻣﻌﮫ ﻓﻲ اﻟﻌﺮوض اﻻﺧﯿﺮة اﻟﺴﺎﺑﻘﺔ اﻻرﺗﻔﺎع /ﺑﻌﺪ اﻟﺨﻂ او اﻧﮫ اﻧﺤﺪار اﻟﺨﻂ و ھﺬا ﯾﻌﻨﻲ ﻣﻜﺎن اﻟﺘﻘﺎطﻊ ﻣﻊ x = 0،وﺗﺬﻛﺮ ان x = 0 --اذا ﺣﺼﻠﺖ ﻋﻠﻰ x = 0وطﺮﯾﻘﺔ اﻟﺘﺤﻘﻖ ﻣﻦ ذﻟﻚ ھﻮ ﺗﻌﻮﯾﺾ yھﻮ ﺗﻘﺎطﻊ bاﻟﺘﺤﻘﻖ ﻣﻦ ان ﺳﺘﻜﻮن ﻋﻠﻰ ،bاذاً اﻟﻨﻘﻄﺔ b 0ﺳﺘﺴﺎوي yﺛﻢ ان mوﻟﻦ اھﺘﻢ ﻟﻘﯿﻤﺔ y = m × 0 + b m × 0 = 0ﻓﮭﺬه اﻟﻤﻌﺎدﻟﺔ ﺳﺘﺼﺒﺢ x = 0،اذا ﻛﺎﻧﺖ yﻣﺤﻮر ھﻮ اﻟﻤﯿﻞ m ،ﺳﻨﺮى ذﻟﻚ ﺑﺎﺳﺘﺨﺪام اﻋﺪاد ﻓﻌﻠﯿﺔ ﻓﻲ اﻟﻌﺮوض اﻟﻘﺎدﻣﺔ ﺣﺘﻰ اﺛﺒﺖ ﻟﻜﻢ ان y = bﻋﻨﺪ اﻟﻨﻘﻄﺔ yواﻟﺨﻂ ﺳﯿﺘﻘﺎطﻊ ﻣﻊ ﻣﺤﻮر ،bھﺬا اﻟﺨﻂ 0 او اﻧﮭﺎ y = m × 1ﺳﻨﺤﺼﻞ ﻋﻠﻰ x = 1؟ ﻋﻨﺪﻣﺎ x = 1ﺗﻘﻊ ﻋﻠﻰ اﻟﺨﻂ ﻣﺎذا ﯾﺤﺪث ﻋﻨﺪﻣﺎ ,bدﻋﻮﻧﺎ ﻧﺤﺎول ﻣﻊ ﺑﻌﺾ اﻻﻋﺪاد ﻧﺤﻦ ﻧﻌﻠﻢ ان اﻟﻨﻘﻄﺔ 0 ﻓﻤﺎ ھﻮ اﻟﻤﯿﻞ ﺑﯿﻦ ﺗﻠﻚ اﻟﻨﻘﻄﺔ وﺗﻠﻚ اﻟﻨﻘﻄﺔ؟؟ دﻋﻮﻧﺎ yاﯾﻀﺎ ً ﺗﻘﻊ ﻋﻠﻰ اﻟﺨﻂ ﺻﺤﯿﺢ؟ ھﺬه ھﻲ ﻗﯿﻤﺔ ,m + bوﻧﻌﻠﻢ اﯾﻀﺎ ً ان اﻟﻨﻘﻄﺔ m + b 1ﺗﺴﺎوي ﻧﺴﺘﺨﺪم ﻧﻘﻄﺘﺎن ﺗﻠﻚ xاﻟﺘﻐﯿﺮ ﻓﻲ y /اي 0 - 1 /ھﺬا ھﻮ اﻟﺘﻐﯿﺮ ﻓﻲ xاﻟﺘﻐﯿﺮ ﻓﻲ y، m + b - b /اﻟﺘﻐﯿﺮ ﻓﻲ m + bﻧﺄﺧﺬ ھﺬه ﻛﻨﻘﻄﺔ ﻧﮭﺎﯾﺔ ،اذاً ﻟﺪﯾﻨﺎ اﺗﻤﻨﻰ اﻧﻜﻢ راﺿﯿﻦ اﻵن واﻧﻨﻲ mاي ﯾﺴﺎوي m/1،ﻓﻨﺤﺼﻞ ﻋﻠﻰ ، b - b = 0 1 - 0 = 1ھﻲ ﻧﻘﻄﺔ اﻟﻨﮭﺎﯾﺔ وﺗﻠﻚ ھﻲ ﻧﻘﻄﺔ اﻟﺒﺪاﯾﺔ اذا ﻗﻤﺖ ﺑﺘﺒﺴﯿﻄﮫ واﻵن ،ﻣﺎ ارﯾﺪ ﻓﻌﻠﮫ ﻓﻲ ھﺬا yﻟﻢ ازﻋﺠﻜﻢ ﺑﺘﺤﺪﯾﺪه ﻋﻦ طﺮﯾﻖ اﺳﺘﺨﺪام ﻛﻞ ھﺬه اﻟﻤﺘﻐﯿﺮات ھﻨﺎ ﻟﻜﻨﮫ ﺳﯿﻌﻄﯿﻨﺎ اﻟﻤﯿﻞ ﺑﻼ ﺷﻚ وھﺬا ﺳﯿﻜﻮن ﺗﻘﺎطﻊ وﻣﻦ ﺛﻢ ﻧﻌﺮف اﻟﻤﻌﺎدﻟﺔ yاﻟﺘﻤﺮﯾﻦ ھﻮ اﻟﻨﻈﺮ اﻟﻰ ھﺬه اﻟﺮﺳﻮﻣﺎت اﻟﺒﯿﺎﻧﯿﺔ ﺛﻢ اﻻﺳﺘﻌﺎﻧﺔ ﺑﮭﺎ ﻓﻲ اﯾﺠﺎد اﻟﻤﻌﺎدﻟﺔ ﺳﻨﻨﻈﺮ اﻟﻰ ھﺬه ،ﺳﻨﺠﺪ اﻟﻤﯿﻞ وﻧﺠﺪ ﺗﻘﺎطﻊ ؟ دﻋﻮﻧﺎ ﻧﺒﺪأ ﺑﻨﻘﻄﺔ ﻋﺸﻮاﺋﯿﺔ دﻋﻮﻧﺎ ﻧﺒﺪأ ﻣﻦ ھﻨﺎ ﻧﺮﯾﺪ اﻟﺤﺼﻮل ﻋﻠﻰ اﻋﺪاد زوﺟﯿﺔ اذا اﻧﺘﻘﻠﻨﺎ اﻟﻰ 3 ،2 ،1اذا ﻛﺎﻧﺖ Aﻣﺎ ھﻮ ﻣﯿﻞ A.ﻟﻨﺒﺪأ اذاً ﺑﺎﻟﺨﻂ ﻧﺬھﺐ ﻟﻼﺳﻔﻞ ﺑﻤﻘﺪار y = --2- = --2اﻧﺎ اﻓﻌﻞ ھﺬا ﻷﻧﻨﻲ ارﯾﺪ اﻟﺤﺼﻮل ﻋﻠﻰ ﻋﺪد زوﺟﻲ ھﻨﺎ --دﻟﺘﺎ y --اﻟﯿﺲ ﻛﺬﻟﻚ؟ 3 ،2 ،1دﻟﺘﺎ x = 3دﻟﺘﺎ اذاً اﻟﻤﯿﻞ ھﻮ -2/3ﻋﻨﺪﻣﺎ ﻧﻨﺘﻘﻞ اﻟﻰ اﻻﻋﻠﻰ y = -2ﻓﺈن اﻟﺘﻐﯿﺮ ﻓﻲ x = 3،ﻋﻨﺪﻣﺎ ﯾﻜﻮن اﻟﺘﻐﯿﺮ ﻓﻲ xﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺘﻐﯿﺮ ﻓﻲ yﻓﺈن اﻟﺘﻐﯿﺮ ﻓﻲ A،ﺑﺎﻟﻨﺴﺒﺔ ﻟـ ﺑﻤﻘﺪار ،3ﺳﻨﻨﺘﻘﻞ اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 2او اذا اﻧﺘﻘﻠﻨﺎ اﻟﻰ اﻻﻋﻠﻰ ﺑﻤﻘﺪار ،1ﻓﺴﻨﻨﺘﻘﻞ اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 2/3ﻻ ﯾﻤﻜﻦ ان ﻧﺮى ھﺬا ھﻨﺎ ﺑﺎﻟﻀﺒﻂ ،ﻟﻜﻨﻚ اي bواﻵن ﻣﺎ ﻗﯿﻤﺔ mھﺬا yﺑﻼ ﺷﻚ ﺗﺮاه ﻋﻨﺪﻣﺎ ﺗﻨﺘﻘﻞ اﻟﻰ اﻻﻋﻠﻰ ﺑﻤﻘﺪار 3ھﺬا ھﻮ اﻟﻤﯿﻞ ﻟﻘﺪ اﻧﺠﺰﻧﺎ ﻧﺼﻒ ھﺬه اﻟﻤﺴﺄﻟﺔ اﻵن ﻋﻠﯿﻨﺎ اﯾﺠﺎد ﺗﻘﺎطﻊ ﻋﻨﺪﻣﺎ ﻧﻨﺘﻘﻞ اﻟﻰ اﻻﻋﻠﻰ ﺑﻤﻘﺪار ،1ﻓﯿﻤﻜﻦ y = 2؟ ﺣﺴﻨﺎ ً ،ﻟﻘﺪ ﻗﻠﻨﺎ ﺑﺎﻟﻔﻌﻞ ان اﻟﻤﯿﻞ ھﻮ 2/3اذاً ھﺬه اﻟﻨﻘﻄﺔ yﺣﺴﻨﺎ ً ،اي ﯾﺘﻘﺎطﻊ ھﺬا ﻣﻊ ﻣﺤﻮر yﺗﻘﺎطﻊ ھﻨﺎ اﻛﺜﺮ y = 4/3ان ﻧﻨﺘﻘﻞ اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 2/3اذاً ھﺬه اﻟﻨﻘﻄﺔ ﯾﺠﺐ ان ﺗﻜﻮن 1/3 1او ﺑﻄﺮﯾﻘﺔ اﺧﺮى ،ﯾﻤﻜﻦ ان ﻧﻘﻮل اﻧﮫ 4/3ﺗﻠﻚ اﻟﻨﻘﻄﺔ ھﻲ دﻋﻮﻧﺎ ﻧﺠﺪ Aاي 4/3 +ھﺬه ھﻲ اﻟﻤﻌﺎدﻟﺔ y = m 2/3-، x + b،ﺳﻨﻌﺮف ان اﻟﻤﻌﺎدﻟﺔ ھﻲ b = 4/3ﻣﻦ 1ﺑﻘﻠﯿﻞ 1/3 1ﺗﻘﺮﯾﺒﺎ ً ﻓﯿﻤﻜﻦ ان ﻧﻘﻮل ان دﻋﻮﻧﺎ اوﻻً ﻧﺠﺪ ﻣﯿﻠﮭﺎ .دﻋﻮﻧﺎ ﻧﺒﺪأ ﻋﻨﺪ ﻧﻘﻄﺔ ﻣﻌﯿﻨﺔ ﯾﻤﻜﻦ ان ﻧﺒﺪا ﻋﻨﺪ ھﺬه اﻟﻨﻘﻄﺔ Bاﺗﻤﻨﻰ ان ﻻ ﻧﺘﻌﺎﻣﻞ ﻣﻊ اﻟﻌﺪﯾﺪ ﻣﻦ اﻟﻜﺴﻮر ھﻨﺎ اﻟﻤﻌﺎدﻟﺔ Bاﻟﻤﻌﺎدﻟﺔ ھﻮ 1ﻋﻨﺪﻣﺎ ﻧﺘﺤﺮك ﺑﻤﻘﺪار 1اﻟﻰ اﻟﯿﻤﯿﻦ ،ﻣﺎذا xاذاً دﻟﺘﺎ xدﻋﻮﻧﻲ اﻛﺘﺐ ﺑﮭﺬه اﻟﻄﺮﯾﻘﺔ ،دﻟﺘﺎ x = --ﻋﻨﺪﻣﺎ دﻟﺘﺎ Bاﻟﻤﻌﺎدﻟﺔ Bدﻋﻮﻧﻲ اﺣﻠﮭﺎ ھﻨﺎ ھﻮ x 1ﻋﻨﺪﻣﺎ ﻧﺬھﺐ اﻟﻰ اﻟﯿﻤﯿﻦ ﺳﯿﻜﻮن اﻟﺘﻐﯿﺮ ﻓﻲ x،دﻟﺘﺎ y /ھﻮ 3اذاً دﻟﺘﺎ yاﻟﺘﻐﯿﺮ ﻓﻲ yدﻟﺘﺎ x؟ ﻧﻨﺘﻘﻞ اﻟﻰ اﻻﻋﻠﻰ ﺑﻤﻘﺪار 3دﻟﺘﺎ yﺳﯿﺤﺪث ﻟﺪﻟﺘﺎ
ﻛﺎﻧﺖ ھﺬه اﺳﮭﻞ ﺑﻌﺾ اﻟﺸﯿﺊ اﻟﻤﻌﺎدﻟﺔ ھﻨﺎ b = 1اذاً y = 1ﻓﺈن x = 0،؟ ﺣﺴﻨﺎ ً ،ﻋﻨﺪﻣﺎ yھﻮ ﻣﻮﺟﺐ 3اذاً اﻟﻤﯿﻞ = 3ﻣﺎ ھﻮ ﺗﻘﺎطﻊ yاﻟﺘﻐﯿﺮ ﻓﻲ b = -2اذاً y = -2ﻓﺈن x = 0،ﻋﻨﺪﻣﺎ y --اوﻻً .ﻛﻤﺎ ﺗﺮى ﻓﺈن ﺗﻘﺎطﻊ yدﻋﻮﻧﺎ ﻧﺠﺪ ﺗﻘﺎطﻊ C،دﻋﻮﻧﺎ ﻧﻔﻌﻞ اﻟﺨﻂ اﻻﺧﯿﺮ اﻟﺨﻂ y = 3x + 1ھﻲ ﻣﺎ ھﻮ اﻟﺘﻐﯿﺮ x = 4اذا ذھﺒﻨﺎ اﻟﻰ اﻟﯿﻤﯿﻦ ﺑﻤﻘﺪار 4 ،3 ،2 ،1اذاً اﻟﺘﻐﯿﺮ ﻓﻲ yدﻋﻮﻧﺎ ﻧﺒﺪأ ﻋﻨﺪ ﺗﻘﺎطﻊ xاﻟﺘﻐﯿﺮ ﻓﻲ y /اﻟﺘﻐﯿﺮ ﻓﻲ = mوﻣﺎ ھﻮ اﻟﻤﯿﻞ؟ = yاذاً اﻟﻤﯿﻞ = 2،4 ،1/2اﻟﻤﻌﺎدﻟﺔ ھﻨﺎ ھﻲ x = 4ھﻮ 2-ﻋﻨﺪﻣﺎ ﯾﻜﻮن اﻟﺘﻐﯿﺮ ﻓﻲ yھﻮ 2-اذاً اﻟﺘﻐﯿﺮ ﻓﻲ yھﻮ 2-اﻟﺘﻐﯿﺮ ﻓﻲ y؟ اﻟﺘﻐﯿﺮ ﻓﻲ yﻓﻲ yھﺬا ھﻮ اﻟﻤﯿﻞ 2- ،واﻧﺘﮭﯿﻨﺎ اﻵن دﻋﻮﻧﺎ ﻧﻨﺘﻘﻞ اﻟﻰ اﻻﺗﺠﺎه اﻵﺧﺮ دﻋﻮﻧﺎ ﻧﻨﻈﺮ اﻟﻰ ﺑﻌﺾ ﻣﻌﺎدﻻت اﻟﺨﻄﻮط وﻧﻌﺮف ان ھﺬا اﻟﻤﯿﻞ وھﺬا ﺗﻘﺎطﻊ 1/2x، x = 0،ھﻮ 5ﻋﻨﺪﻣﺎ yودﻋﻮﻧﺎ ﻧﻘﻮم ﺑﺘﻤﺜﯿﻠﮭﻢ ﺑﯿﺎﻧﯿﺎ ً دﻋﻮﻧﺎ ﻧﺒﺪأ ﺑﮭﺬا اﻟﺨﻂ اوﻻً ﻟﻘﺪ ﺑﺪأت ﻓﻌﻼً ﺑﺘﺤﻮﯾﻄﮫ ﺑﺎﻟﻠﻮن اﻟﺒﺮﺗﻘﺎﻟﻲ ﺗﻘﺎطﻊ b--وذاك mذﻟﻚ-- واﻟﻤﯿﻞ ھﻮ 2ھﺬا ﯾﻌﻨﻲ اﻧﮫ ﻋﻨﺪﻣﺎ اﺗﺤﺮك yھﺬا ھﻮ ﺗﻘﺎطﻊ y = 1، 2، 3 4، 5ﻓﺈن x = 0،ﯾﻤﻜﻨﻚ اﻟﺘﺤﻘﻖ ﻣﻦ ذﻟﻚ ﻓﻲ اﻟﻤﻌﺎدﻟﺔ ﻓﻌﻨﺪﻣﺎ y = 5ﻓﺈن x،اذا ﺗﺤﺮﻛﺖ اﻟﻰ 1ﺑﺎﺗﺠﺎه yﻓﺴﺄﺗﺤﺮك ﻟﻠﻌﻠﻰ ﺑﻤﻘﺪار 2ﺑﺎﺗﺠﺎه x،اذا ﺗﺤﺮﻛﺖ اﻟﻰ 1ﺑﺎﺗﺠﺎه yﺳﺄﺗﺤﺮك ﻟﻼﻋﻠﻰ ﺑﻤﻘﺪار 2ﺑﺎﺗﺠﺎه x،ﺑﻤﻘﺪار 1ﺑﺎﺗﺠﺎه اذا اﺗﺠﮭﺖ رﺟﻮﻋﺎ ً اﻟﻰ 1ﺑﺎﺗﺠﺎه yﻓﺴﺄﺗﺤﺮك اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 2ﺑﺎﺗﺠﺎه x،واذا اﺗﺠﮭﺖ رﺟﻮﻋﺎ ً اﻟﻰ 1ﺑﺎﺗﺠﺎه yﺳﺄﺗﺤﺮك ﻟﻼﻋﻠﻰ ﺑﻤﻘﺪار 2ﺑﺎﺗﺠﺎه ﺳﺄﺳﺘﻤﺮ ﻓﻲ ﻓﻌﻞ ذﻟﻚ اذاً ھﺬا اﻟﺨﻂ ﺳﯿﺒﺪو --ﻻ ﯾﻤﻜﻨﻨﻲ ان ارﺳﻢ اﻟﺨﻄﻮط ﺑﺄﺳﻠﻮب ﻣﺘﻘﻦ ﺟﺪاً ،ﻟﻜﻨﮫ yﻓﺴﺄﺗﺤﺮك اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 2ﺑﺎﺗﺠﺎه x، ﺳﯿﻜﻮن اﻓﻀﻞ ﻣﺎ ﯾﻤﻜﻨﻨﻲ ﻓﻌﻠﮫ ﺳﯿﺒﺪو ھﻜﺬا ﺳﺎﺳﺘﻤﺮ اﻛﺜﺮ واﻛﺜﺮ ھﺬا ھﻮ اﻟﺨﻂ اﻻول ﯾﻤﻜﻨﻨﻲ اﻻﺳﺘﻤﺮار ﺑﺎﻟﻨﺰول اﻟﻰ اﺳﻔﻞ ھﻜﺬا دﻋﻮﻧﺎ ﻧﺮﺳﻢ ھﺬا y = -1/5x +ﻣﻦ اﻟﺴﮭﻞ داﺋﻤﺎ ً ان ﺗﻔﻜﺮ ﻓﻲ اﻟﻜﺴﻮر اذاً 0.2ﺗﻌﺎدل 1/5ﻓﯿﻤﻜﻦ ان ﻧﻜﺘﺐ ، y = -0.2x + 7دﻋﻮﻧﻲ اﻛﺘﺐ ھﺬا y = -0.2x + 7اﻟﺨﻂ ھﺬا ﯾﻮﺿﺢ اﻧﮫ ﻟﻜﻞ 5ﻧﺘﺤﺮﻛﮭﺎ اﻟﻰ اﻟﯿﻤﯿﻦ ﺳﻨﺘﺤﺮك اﻟﻰ x = 0ﻋﻨﺪﻣﺎ yﻟﮫ ھﻮ 7اي اﻧﮫ 6 ،5 ،4 ،3 ،2 ،1ھﺬا ھﻮ ﺗﻘﺎطﻊ yوﻧﻌﻠﻢ ان ﺗﻘﺎطﻊ 7 ﻟﻜﻞ 5ﻧﺘﺤﺮﻛﮭﺎ اﻟﻰ اﻟﯿﻤﯿﻦ ،ﺳﻨﺘﺤﺮك ﺑﻤﻘﺪار 1اﻟﻰ اﻻﺳﻔﻞ ﻟﻜﻞ 5اذاً x = -1/5 5 ،4 ،3 ،2 ،1دﻟﺘﺎ y /اﻻﺳﻔﻞ ﺑﻤﻘﺪار 1ﯾﻤﻜﻨﻨﺎ اﻋﺘﺒﺎره -1/5دﻟﺘﺎ ﻧﺘﺤﺮك 5اﻟﻰ اﻟﯿﻤﯿﻦ ھﺬا ﯾﻌﻨﻲ ان ﻋﻠﯿﻨﺎ ان ﻧﺘﺤﺮك اﻟﻰ اﻻﺳﻔﻞ ﺑﻤﻘﺪار 1ﻧﺘﺤﺮك 5اﻟﻰ اﻟﯿﻤﯿﻦ 5 ،4 ،3 ،2 ،1ﻋﻠﯿﻨﺎ ان ﻧﺘﺤﺮك ﺑﻤﻘﺪار 1اﻟﻰ اﻻﺳﻔﻞ واذا ﻋﺪﻧﺎ ،اي اذا ﺗﺤﺮﻛﻨﺎ ﺑﻤﻘﺪار 5اﻟﻰ اﻟﻮراء --ﺑﺪﻻً ﻣﻦ ھﺬا ،اذا اﻋﺘﺒﺮﺗﮫ 1/5ﻓﺈن ھﺬه ﺑﻜﻞ وﺿﻮح اﻋﺪاد ﻣﺘﺴﺎوﯾﺔ اذا ﻋﺪﻧﺎ ﺑﻤﻘﺪار -- 5ھﺬه ،1 5- 5 ،4 ،3 ،2ﺑﺎﻟﺘﺎﻟﻲ ﺳﻨﺘﺤﺮك ﺑﻤﻘﺪار 1اﻟﻰ اﻻﻋﻠﻰ اذا ﻋﺪﻧﺎ ﺑﻤﻘﺪار --5 4 ،3 ،2 ،1-- 5ﺳﻨﺘﺤﺮك اﻟﻰ اﻻﻋﻠﻰ ﺑﻤﻘﺪار 1اذاً اﻟﺨﻂ ﺳﯿﺒﺪو ھﻜﺬا ﻋﻠﻲ = ، yﻓﻘﻂ ان اﺻﻞ اﻟﻨﻘﺎط اﻋﺘﻘﺪ اﻧﻚ اﺳﺘﻮﻋﺒﺖ اﻟﻔﻜﺮة ﻋﻠﻲ ﻓﻘﻂ ان اﺻﻞ ﺗﻠﻚ اﻟﻨﻘﺎط ﻻ ﯾﻤﻜﻨﻨﻲ رﺳﻤﮫ ﺑﺼﻮرة ﻣﺴﺘﻘﯿﻤﺔ ﻗﻠﯿﻼً واﻵن دﻋﻮﻧﺎ ﻧﺮﺳﻢ ھﺬا b = 0ﻓﯿﻤﻜﻨﻚ ان ﺗﻌﺘﺒﺮھﺎ 0 +ﻓﮭﻨﺎ ، b = 0؟ ﺣﺴﻨﺎ ً bاﯾﻦ y = mx + bﺗﺘﺬﻛﺮون ﺑﺄﻧﻨﺎ ﻗﻠﻨﺎ ان b؟ ﻻ ارى اي ﻋﺒﺎرة ﻟـ bاﯾﻦ ﻋﺒﺎرة -x y = -x اذاً اﻟﻤﯿﻞ x + 0-ھﻨﺎ ﻋﻠﻰ ﻧﻘﻄﺔ اﻻﺻﻞ ﺛﻢ اﻟﻤﯿﻞ --ﻣﺮة اﺧﺮى ﺳﻨﺮى اﺷﺎرة ﺳﺎﻟﺒﺔ ﯾﻤﻜﻨﻚ اﻋﺘﺒﺎرھﺎ y، 1ھﺬا ھﻮ ﺗﻘﺎطﻊ y = 0ﻓﺈن x = 0،ﻋﻨﺪﻣﺎ ﺳﻨﺘﺤﺮك x،ﯾﻜﻮن 1-ﻋﻨﺪﻣﺎ ﻧﺘﺤﺮك اﻟﻰ اﻟﻌﻠﻰ ﺑﻤﻘﺪار 1ﻋﻠﻰ yھﻮ 1ﻓﺎﻟﺘﻐﯿﺮ ﻓﻲ xھﻮ 1-ﻋﻨﺪﻣﺎ ﻧﺘﺤﺮك اﻟﻰ اﻟﯿﻤﯿﻦ ﺑﻤﻘﺪار ،1ﻋﻨﺪﻣﺎ اﻟﺘﻐﯿﺮ ﻓﻲ اﺷﺎرات ﻣﺘﻀﺎدة ﯾﺘﺠﮭﺎن yو xﺣﯿﺚ ان ﻟـ y،ﻓﺴﺘﺘﺤﺮك ﻟﻼﻋﻠﻰ ﺑﻤﻘﺪار 1ﻋﻠﻰ x،او اذا ﺗﺤﺮﻛﺖ ﻟﻼﺳﻔﻞ ﺑﻤﻘﺪار 1ﻋﻠﻰ yﻟﻸﺳﻔﻞ ﺑﻤﻘﺪار 1ﻋﻠﻰ y = 3.75ﺑﺎﺗﺠﺎھﺎت ﻣﺘﻌﺎﻛﺴﺔ اذاً اﻟﺨﻂ ﺳﯿﺒﺪو ھﻜﺬا ﯾﻤﻜﻨﻚ ان ﺗﺘﺨﯿﻞ اﻧﮫ ﯾﻘﺴﻢ اﻟﺮﺑﻌﯿﻦ اﻟﺜﺎﻧﻲ واﻟﺮاﺑﻊ اﻵن ﺳﺄﺣﻞ ﻣﺴﺄﻟﺔ اﺧﺮى دﻋﻮﻧﺎ ﻧﺤﻞ ھﺬه = y؟ اﻧﮭﺎ ﻏﯿﺮ ﻣﻮﺟﻮدة ﺣﺴﻨﺎ ً ،ﻓﻲ اﻟﺤﻘﯿﻘﺔ ھﻨﺎ ،ﯾﻤﻜﻦ اﻋﺎدة ﻛﺘﺎﺑﺔ اﻟﻤﻌﺎدﻟﺔ ﻟﺘﺼﺒﺢ xاي ﻋﺒﺎرة y = mx + bورﺑﻤﺎ اﻧﻚ ﺗﻘﻮل اﻵن ،ﺳﻨﻨﻈﺮ اﻟﻰ ﺣﯿﺚ xﻻ اھﺘﻢ ﻟﻤﻘﺪار اﻟﺘﻐﯿﺮ ﻓﻲ x = 0دﻟﺘﺎ y /ﻻ ﯾﺘﻐﯿﺮ دﻟﺘﺎ yﺣﯿﺚ ان x،اﻵن اﺻﺒﺤﺖ ﻣﻨﻄﻘﯿﺔ اﻟﻤﯿﻞ ھﻮ 0ﻻ ﯾﮭﻢ ﻣﻘﺪار اﻟﺘﻐﯿﺮ ﻓﻲ 0x + 3.75 ﺳﺘﻜﻮن داﺋﻤﺎ ً y 3.75ﻟﻦ ﺗﺘﻐﯿﺮ ،ﺣﯿﺚ ان yﻓﺈن x،ھﻮ 3.75اذاً 3.75 ,2 ,1ﺗﻘﻊ ھﻨﺎ ﻋﻠﯿﻚ اﻻﻗﺘﺮاب ﻣﻨﮭﺎ 3/4 3وﻣﮭﻤﺎ ﻛﺎن اﻟﺘﻐﯿﺮ ﻓﻲ yﺗﻘﺎطﻊ . United States Military Academy, West Point.ﻋﻠﻰ اي ﺣﺎل ،اﺗﻤﻨﻰ اﻧﻜﻢ وﺟﺪﺗﻢ ھﺬا ﻣﻔﯿﺪاً y = 3.75ﺳﯿﻜﻮن اﻟﺨﻂ اﻓﻘﯿﺎ ً ﻋﻠﻰ
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