WEBVTT

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မ်ဥ္းတစ္ေၾကာင္းက (-3,6) ႏွင့္ (6,0) ဆိုုတဲ့ အမွတ္ေတြကိုုၿဖတ္သြားတယ္.

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အဲ့ဒီမ်ဥ္းအတြက္ equation ကိုု point slope form, slope intercept form,

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 ႏွင့္ standard form ပံုုစံတိုု႔ျဖင့္ရွာေပးပါ.

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ဒါကေတာ့

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equation တစ္ေၾကာင္းထဲကိုု 3 မ်ိုဳးေရးတာနဲ႔ တူတူပါပဲ.

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ဒီ 3 မ်ိဳးထဲက 1 မ်ိုဳး ကိုုရရင္, က်န္တဲ့ 2 မ်ိဳးကိုု

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ျပန္ေၿပာင္းေရးႏိုုင္ပါၿပီ.

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ဒါေပမယ့္ အဲဒါေတြက ဘာေတြလဲဆိုုရင္, point slope form ဆိုုတာ

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x1 ႏွင့္ y1 က မ်ဥ္းတစ္ေၾကာင္းေပၚက

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အမွတ္ေတြဆိုုပါေတာ့

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ဒီစာလံုုးေတြေအာက္နားက ခပ္ေသးေသးေရးထားတာကေတာ့

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တကယ္လိုု႔ x တစ္လုုံးပဲေရးထားရင္ေတာ့, ကြ်န္ေတာ္တုုိ႔က

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ဘယ္တန္ဖိုုးမဆိုုၿဖစ္ႏိုုင္တဲ့ ကိန္းရွင္တစ္ခုုကိုုေၿပာေနတာၿဖစ္ပါတယ္.

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တကယ္လိုု႔ x ႏွင့္ y ေအာက္နားေတြမွာ 1 ခပ္ေသးေသးေလးေတြေရးထားတယ္ ဆိုုရင္ေတာ့

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ဒါဟာ သီးသန္႔တန္ဖိုုးရွိတဲ့ x သိုု႔မဟုုတ္ y, ဒါမွမဟုုတ္

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coordinate တန္ဖိုုးတစ္ခုုကိုုဆိုုလုုိတာ ျဖစ္ပါတယ္.

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ကြ်န္ေတာ္တိုု႔ ဥပမာတြက္ရင္ ျမင္ရပါလိမ့္မယ္.

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ဒါေပမယ့္ point slope form ဆိုုတာက

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အမွတ္တစ္ခုု နဲ႔ မ်ဥ္းေၾကာင္းရဲ႕ slope ကိုုသိတယ္ ဆိုုပါေတာ့

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ဒါဆိုု အဲဒီ မ်ဥ္းကိုု point slope form နဲ႔ ေရးရရင္

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y-y1 = m*(x-x1)

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ဥပမာအားၿဖင့္

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(-3,6)ဆိုုတဲ့ အမွတ္က မ်ဥ္းေပၚမွာဆုုိရင္ 

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y-6= m(x-(-3)) လိုု႔ေၿပာလိုု႔ရပါတယ္

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ဒါဆိုု (x+3) ျဖစ္သြားပါမယ္.

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ဒါဟာ သီးသန္႔တန္ဖိုုးရွိတဲ့ x နဲ႔ y ပါ။

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ဒီေနရာမွာေတာ့ -3 နဲ႔ 6 ပါ။

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ဒါကေတာ့ point slope form ေပါ့။

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Slope intercept form ကေတာ့ y=mx+b

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ဒီမွာလည္း m က slope, b က 5y-၀င္ရိုုးကိုုၿဖတ္တဲ့အမွတ္

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တစ္နည္းအားၿဖင့္ x ကသုုညၿဖစ္တဲ့အခ်ိန္မွာရွိေနတဲ့

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y ရဲ႕တန္ဖိုုးပါ။

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Standard form ကေတာ့ ax+by=c,

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ဒါေတြက အေျခခံအားျဖင့္ ကိန္းဂဏန္း ၂ခုုပါပဲ။

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သုူတိုု႔က graph ေပၚမွာ

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တိုုက္ရိုုက္ပတ္သတ္မွဳမ်ိုဳးမရွိပါဘူး

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ကဲ ဒီ forms ေတြကိုု အေၿဖရွာၾကည့္ၾကပါစိုု႔

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ပထမဆံုုး slope ကိုုအရင္ရွာပါမယ္။

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Slope ကိုုသိၿပီဆိုုရင္ point slope form က

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တြက္ရတာ တကယ္ကိုု အရမ္းလြယ္သြားပါျပီ

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slope ျဖစ္တဲ့

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m  က y ေျပာင္းလဲမွဳကိုု x ေၿပာင္းလဲမွဳနဲ႔ စားတာပါ။

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ဒါဆိုု y ေၿပာင္းလဲမွဳဆိုုတာ ဘာလဲ?

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ဒါကိုု ကြ်န္ေတာ္တိုု႔ရဲ႕အဆံုုးမွတ္လိုု႔သေဘာထားရင္

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ကြ်န္ေတာ္တိုု႔က ဒီကေနအဲဒီအမွတ္ကိုုသြားတယ္ဆိုုရင္

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y ေျပာင္းလဲမွဳကဘာလဲ?

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ကြ်န္ေတာ္တိုု႔မွာ 0 ဆိုုတဲ့အဆံုုးမွတ္တစ္ခုုရွိမယ္။ y က 6 ကစၿပီး

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0 မွာဆံုုးတယ္။

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ဒါဆိုု y ရဲ႕ ဆံုုးမွတ္က 0 ျဖစ္ၿပီး၊ စမွတ္က 6 ျဖစ္တယ္။

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ကြ်န္ေတာ္တိုု႔ xရဲ႕ ဆံုုးမွတ္ ဒါမွမဟုုတ္ x-coordinate ကဘာလဲ?

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x-coordinate က 6 ပါ။

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ကြ်န္ေတာ္ရွင္းေအာင္ၿပန္ေၿပာၿပပါမယ္။

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ဒါဆိုု ဒီ 0,

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ေနာက္ၿပီး ကြ်န္ေတာ္တိုု႔မွာ y ရဲ႕ စမွတ္ 6 ရွိတယ္။

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ေဟာဟိုုက 6 ပါ။

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ေနာက္ ကြ်န္ေတာ္တိုု႔က xရဲ႕ ဆံုုးမွတ္ကိုု လိုုခ်င္တယ္။ အဲဒါက ေဟာဒီက 6

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ဒါမွမဟုုတ္ ဒီ 6။ ေနာက္ၿပီး ကြ်န္ေတာ္တိုု႔က

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အဲဒါကိုု xရဲ႕ စမွတ္ကေန ႏွဳတ္ခ်င္တာပါ။

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xရဲ႕ စမွတ္က ေဟာဟိုုမွာပါ

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-3 ပဲျဖစ္ပါတယ္။

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ေသခ်ာေအာင္ျပန္ေျပာရရင္

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ဒီ -3 က ေဟာဟိုုက -3 ပါပဲ။

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ကြ်န္ေတာ္ေျပာတာက ဒီအမွတ္ကေနဒီအမွတ္ကိုုသြားရင္

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y က 6 မွတ္ေလ်ာ့သြားတယ္

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ကြ်န္ေတာ္တိုု႔ 6 ကေန 0 ကိုုေရာက္သြားတယ္။

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ကြ်န္ေတာ္တိုု႔ရဲ႕ y က 6 မွတ္ေလ်ာ့သြားပါတယ္။

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ဒါေၾကာင့္ 0-6 ဆိုုေတာ့ -6 ရပါတယ္။

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.

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y က 6 မွတ္ေလ်ာ့သြားတယ္

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ကြ်န္ေတာ္တိုု႔ ဒီအမွတ္ကေန ဒီအမွတ္ကိုုသြားရင္

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x ကဘာၿဖစ္မလဲ?

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-3 ကေန 6 ကိုုသြားတယ္ဆိုုေတာ့ x က 9 မွတ္တိုုးလာသင့္တာေပါ့

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အဲဒါကိုုတြက္မယ္ဆိုုရင္ -3 ကိုုယူၿပီး 6 ထဲကႏွုဳတ္ရင္

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6 ကိုု 3 ေပါင္းတာနဲ႔ တုူတူပဲေပါ့ 9 ရပါတယ္

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ေနာက္ၿပီး -6 ကိုု 9 နဲ႔စားရင္ ဘယ္ေလာက္ရလဲ

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အဲဒါကိုုရွင္းလိုုက္ရင္ -2/3 က်န္ပါတယ္

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ပိုုင္းေဝေရာ ပိုုင္းေၿခကိုုပါ 3 နဲ႔စားလိုုက္တာပါ

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ဒါဆိုု ဒါဟာကြ်န္ေတာ္တိုု႔ရဲ႕ slope ျဖစ္တဲ့ -2/3 ပါ

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အခုုဆိုု ကြ်န္ေတာ္တိုု႔က point slope form ကိုုအသံုုးၿပဳလိုု႔ရပါၿပီ

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ကြ်န္ေတာ္တိုု႔မွာ အမွတ္တစ္မွတ္ရွိပါတယ္။ ဘယ္အမွတ္မဆိုု သံုုးလိုု႔ရပါတယ္။

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ကြ်န္ေတာ္ကေတာ့ (-3,6) ကိုုပဲသံုုးလိုုက္ပါမယ္

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ကြ်န္ေတာ္တိုု႔မွာ slope လည္းရွိပါတယ္

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point slope form နဲ႔ေရးၾကည့္ရေအာင္

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.

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y ထဲကႏွဳတ္ဖိုု႔ ကြ်န္ေတာ္တိုု႔

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ဒီအမွတ္၂ခုုထဲက ၾကိဳက္တဲ့တစ္ခုုယုူလိုု႔ရပါတယ္. ကြ်န္ေတာ္ကဒီတစ္ခုုယူပါမယ္။

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y minus ေဟာဒီက y ရဲ႕ တန္ဖိုုး, ဒါဆိုု y-6=

99:59:59.999 --> 99:59:59.999
90
00:04:42,990 --> 00:04:51,480
slope တန္ဖိုုးျဖစ္တဲ့ (-2/3) အေၿမွာက္ x minus 

91
00:04:51,480 --> 00:04:51,930
x-coordinate.

92
00:04:51,930 --> 00:04:55,490
x-coordinate က -3

93
00:04:55,490 --> 00:05:00,370
ဆိုုေတာ့ x minus (-3) ဆိုုရင္ရပါၿပီ။

99:59:59.999 --> 99:59:59.999
94
00:05:00,370 --> 00:05:01,570
ဒါကိုုနဲနဲထပ္ရွင္းလိုု႔ရပါေသးတယ္

99:59:59.999 --> 99:59:59.999
95
00:05:01,570 --> 00:05:08,650
y-6 = -2/3 အေၿမွာက္ x.

99:59:59.999 --> 99:59:59.999
96
00:05:08,650 --> 00:05:12,610
x minus -3 က x +3 နဲ႔တူတူပါပဲ

99:59:59.999 --> 99:59:59.999
97
00:05:12,610 --> 00:05:15,760
ဒါကေတာ့ ကြ်န္ေတာ္တိုု႔ရဲ႕ point slope form ပါ။

99:59:59.999 --> 99:59:59.999
98
00:05:15,760 --> 00:05:19,270
အခုု ကြ်န္ေတာ္တိုု႔က ဒီဟာ ကိုုပဲ 

99
00:05:19,270 --> 00:05:23,500
slope intercept form ကိုု ေျပာင္းလဲလိုုက္လိုု႔ရပါတယ္

99:59:59.999 --> 99:59:59.999
100
00:05:23,500 --> 00:05:24,130
ကဲ လုုပ္ၾကည့္ရေအာင္

99:59:59.999 --> 99:59:59.999
101
00:05:24,130 --> 00:05:27,560
slope intercept ကိုု လိေမာ္ေရာင္နဲ႔ လုုပ္ၾကမယ္ေနာ္

99:59:59.999 --> 99:59:59.999
102
00:05:27,560 --> 00:05:30,960
ကြ်န္ေတာ္တိုု႔မွာ slope intercept ရွိပါတယ္

99:59:59.999 --> 99:59:59.999
103
00:05:30,960 --> 00:05:35,200
.

99:59:59.999 --> 99:59:59.999
104
00:05:35,200 --> 00:05:37,040
ဒီဟာကိုုဘယ္လိုုရွင္းၾကမလဲဆိုုေတာ့

99:59:59.999 --> 99:59:59.999
105
00:05:37,040 --> 00:05:41,510
ကြ်န္ေတာ္တိုု႔က -2/3 ကိုုေၿမွာက္လိုုက္လိုု႔ရပါတယ္။

99:59:59.999 --> 99:59:59.999
106
00:05:41,510 --> 00:05:44,150
ကြ်န္ေတာ္က -2/3 ကိုု အထဲဝင္ေျမွာက္မွာပါ။ y-6=

99:59:59.999 --> 99:59:59.999
107
00:05:44,150 --> 00:05:48,950
-2/3 အေျမွာက္ x က -2/3x ပါ

99:59:59.999 --> 99:59:59.999
108
00:05:48,950 --> 00:05:53,890
-2/3 အေျမွာက္ 3 က -2 ရပါတယ္

99:59:59.999 --> 99:59:59.999
109
00:05:53,890 --> 00:05:56,150
အခုု slope intercept form အေနနဲ႔ရဖိုု႔

99:59:59.999 --> 99:59:59.999
110
00:05:56,150 --> 00:05:59,270
6 ကိုု ၂ဖက္စလုုံးမွာ ေပါင္းလုုိက္မယ္ဆိုု ဘယ္ဖက္အျခမ္းက 6 ကိုု

99:59:59.999 --> 99:59:59.999
111
00:05:59,270 --> 00:06:02,380
ဖယ္ျပီးသားျဖစ္သြားမွာပါ. equation ရဲ႕ ၂ဖက္စလုုံးကိုု

99:59:59.999 --> 99:59:59.999
112
00:06:02,380 --> 00:06:04,400
6 ေပါင္းရေအာင္

99:59:59.999 --> 99:59:59.999
113
00:06:04,400 --> 00:06:06,010
ဘယ္ဘက္အျခမ္းမွာ y တစ္ခုုထဲက်န္ၿပီး

99:59:59.999 --> 99:59:59.999
114
00:06:06,010 --> 00:06:08,090
ဒီေကာင္ေတြကေတာ့ ေၾကသြားမွာပါ

99:59:59.999 --> 99:59:59.999
115
00:06:08,090 --> 00:06:12,830
အခုုဆိုု y= -2/3x

99:59:59.999 --> 99:59:59.999
116
00:06:12,830 --> 00:06:15,810
-2 အေပါင္း 6 က +4 ရပါတယ္

99:59:59.999 --> 99:59:59.999
117
00:06:15,810 --> 00:06:19,890
ဒါကကြ်န္ေတာ္တိုု႔ရဲ႕ slope intercept form ပါ

99:59:59.999 --> 99:59:59.999
118
00:06:19,890 --> 00:06:22,590
mx အေပါင္း b, ဒါက ကြ်န္ေတာ္တိုု႔ y ျဖတ္မွတ္ပါ။

99:59:59.999 --> 99:59:59.999
119
00:06:22,590 --> 00:06:24,480
အခုု ကြ်န္ေတာ္တိုု႔ standard form

99:59:59.999 --> 99:59:59.999
120
00:06:24,480 --> 00:06:25,730
ရွာဖိုု႔ပဲက်န္ပါေတာ့တယ္

99:59:59.999 --> 99:59:59.999
121
00:06:25,730 --> 00:06:30,440
.

99:59:59.999 --> 99:59:59.999
122
00:06:30,440 --> 00:06:32,840
ဒီတစ္ခါလည္း ရွိၿပီးသား equationကိုု ေျပာင္းလုုိက္ရံုုပါပဲ

99:59:59.999 --> 99:59:59.999
123
00:06:32,840 --> 00:06:34,500
x ေရာ y ေရာ equation ရဲ႕

99:59:59.999 --> 99:59:59.999
124
00:06:34,500 --> 00:06:36,130
ဘယ္ဘက္အျခမ္းကိုု ေျပာင္းေပးရမွာပါ

99:59:59.999 --> 99:59:59.999
125
00:06:36,130 --> 00:06:40,140
ဒါဆိုု equation ရဲ႕ ၂ဖက္စလံုုးကိုု 2/3 နဲ႔ေပါင္းၾကရေအာင္

99:59:59.999 --> 99:59:59.999
126
00:06:40,140 --> 00:06:42,140
ကြ်န္ေတာ္ ဒီက စပါမယ္

99:59:59.999 --> 99:59:59.999
127
00:06:42,140 --> 00:06:45,950
ကြ်န္ေတာ္တိုု႔မွာ y = -2/3x +4 ရွိပါတယ္

99:59:59.999 --> 99:59:59.999
128
00:06:45,950 --> 00:06:47,540
ဒါက slope intercept form ပါ

99:59:59.999 --> 99:59:59.999
129
00:06:47,540 --> 00:06:53,790
2/3x ကိုု equation ရဲ႕ ၂ဖက္စလုုံးကိုု

99:59:59.999 --> 99:59:59.999
130
00:06:53,790 --> 00:06:55,040
ေပါင္းၾကရေအာင္

99:59:59.999 --> 99:59:59.999
131
00:06:55,040 --> 00:06:57,650
.

99:59:59.999 --> 99:59:59.999
132
00:06:57,650 --> 00:07:00,060
ကြ်န္ေတာ္ဒီလိုုလုုပ္တာဟာ equation ရဲ႕

99:59:59.999 --> 99:59:59.999
133
00:07:00,060 --> 00:07:02,350
ညာဖက္မွာ ဒီ -2/3x ကိုု မရွိေအာင္လိုု႔ပါ

99:59:59.999 --> 99:59:59.999
134
00:07:02,350 --> 00:07:05,010
equation ရဲ႕ ဘယ္ဖက္အၿခမ္းက

99:59:59.999 --> 99:59:59.999
135
00:07:05,010 --> 00:07:07,730

99:59:59.999 --> 99:59:59.999
136
00:07:07,730 --> 00:07:09,890
အခုုဘာၿဖစ္သြားျပီလဲ?

99:59:59.999 --> 99:59:59.999
137
00:07:09,890 --> 00:07:16,390
2/3x အေပါင္း y, ဒါက ကြ်န္ေတာ့္ equation ရဲ႕

99:59:59.999 --> 99:59:59.999
138
00:07:16,390 --> 00:07:20,220
ဘယ္ဖက္အျခမ္းပါ။ ဒီေကာင္ေတြက ေၾကသြားတယ္ဆိုုေတာ့

99:59:59.999 --> 99:59:59.999
139
00:07:20,220 --> 00:07:22,650
4 ရပါတယ္

99:59:59.999 --> 99:59:59.999
140
00:07:22,650 --> 00:07:25,580
ဒါဆိုု ဒီ standard form ကိုုရပါၿပီ

99:59:59.999 --> 99:59:59.999
141
00:07:25,580 --> 00:07:26,790
.

99:59:59.999 --> 99:59:59.999
142
00:07:26,790 --> 00:07:30,030
အပိုုင္းကိန္းေဖ်ာက္ခ်င္တယ္ဆိုုရင္ေတာ့

99:59:59.999 --> 99:59:59.999
143
00:07:30,030 --> 00:07:32,340
၂ဖက္စလုုံးကိုု 3 နဲ႔ေျမွာက္လိုု႔ရပါတယ္

144
00:07:32,340 --> 00:07:33,860
.

145
00:07:33,860 --> 00:07:36,400
အဲ့လိုုလုုပ္ရင္ ဘာရမလဲ?

99:59:59.999 --> 99:59:59.999
146
00:07:36,400 --> 00:07:40,220
2/3xကိုု 3နဲ႔ေျမွာက္ရင္ 2xရပါတယ္

99:59:59.999 --> 99:59:59.999
147
00:07:40,220 --> 00:07:43,440
yကိုု 3နဲ႔ေျမွာက္ရင္ 3y ရပါတယ္

99:59:59.999 --> 99:59:59.999
148
00:07:43,440 --> 00:07:45,700
4 အေျမွာက္ 3 က 12

99:59:59.999 --> 99:59:59.999
149
00:07:45,700 --> 00:07:47,620
equation ၂ခုုကတူတူပါပဲ။ ၂ဖက္စလုုံးကိုု 3နဲ႔ေျမွာက္လိုုက္တာပါပဲ

99:59:59.999 --> 99:59:59.999
150
00:07:47,620 --> 00:07:48,760

151
00:07:48,760 --> 00:07:50,190
ဘယ္ဖက္အျခမ္းကိုုေျမွာက္ရင္ ညာဖက္ကိုုလည္းေျမွာက္ရမယ္

99:59:59.999 --> 99:59:59.999
152
00:07:50,190 --> 00:07:52,680
.

153
00:07:52,680 --> 00:07:56,160
ဒါဆိုု standard form ရပါၿပီ