$$ a0 ; b

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$$ a>0 ; b<0 ; c<0 $$ bo'lsa, $$ a x+b y+c=0 $$ to'g'ri chiziqning eskizini chizing.

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Agar $$ a > 0 $$, $$ b < 0 $$, va $$ c < 0 $$ bo'lsa, tenglama $$ a x + b y + c = 0 $$ to'g'ri chizig'ini chizish uchun quyidagi qadamlarni bajarish mumkin: 1. **X-interseptini topish:** To'g'ri chiziqning $$ x $$-interseptini topish uchun $$ y = 0 $$ qo'yiladi: $$ a x + c = 0 \implies x = -\frac{c}{a} $$ Berilgan shartlarga ko'ra, $$ a > 0 $$ va $$ c < 0 $$ bo'lganligi sababli, $$ x = -\frac{c}{a} > 0 $$. Demak, $$ x $$-intersept musbat $$ x $$-o'qida joylashgan. 2. **Y-interseptini topish:** To'g'ri chiziqning $$ y $$-interseptini topish uchun $$ x = 0 $$ qo'yiladi: $$ b y + c = 0 \implies y = -\frac{c}{b} $$ $$ b < 0 $$ va $$ c < 0 $$ bo'lgani uchun, $$ y = -\frac{c}{b} < 0 $$. Demak, $$ y $$-intersept manfiy $$ y $$-o'qida joylashgan. 3. **Gradientni aniqlash:** Tenglamani $$ y = kx + m $$ shaklida qayta yozamiz: $$ y = -\frac{a}{b}x - \frac{c}{b} $$ Bu yerda gradient $$ k = -\frac{a}{b} $$ bo'lib, $$ a > 0 $$ va $$ b < 0 $$ bo'lgani uchun, $$ k > 0 $$. Demak, to'g'ri chiziq ijobiy gradientga ega. 4. **Grafikni chizish:** - **X-intersept nuqtasi:** $$ A \left( \frac{-c}{a}, 0 \right) $$ - **Y-intersept nuqtasi:** $$ B \left( 0, \frac{-c}{b} \right) $$ Ushbu ikki nuqtani bog'lab to'g'ri chiziq chizamiz. Gradient ijobiy bo'lgani sababli, chiziq chapdan o'ngga qarab yuqoriga ko'tariladi. Grafik quyidagicha bo'ladi: ``` y | | / | / | / | / | / |____/________ x A ``` **Izoh:** - Chiziqning $$ x $$-intersepti musbat $$ x $$-o'qida ($$ A $$ nuqtasi), va $$ y $$-intersepti manfiy $$ y $$-o'qida joylashgan. - Chiziq to'rtinchi kvadrantdan birinchi kvadrantga yaqinlashadi, chunki gradient ijobiy. Shu tarzda, berilgan shartlar asosida $$ a x + b y + c = 0 $$ tenglamasining grafigi muvaffaqiyatli chiziladi. To'g'ri chiziqning eskizini chizish uchun: 1. **X-interseptini toping:** $$ x = -\frac{c}{a} $$ (musbat $$ x $$-o'qida joylashgan). 2. **Y-interseptini toping:** $$ y = -\frac{c}{b} $$ (manfiy $$ y $$-o'qida joylashgan). 3. **Gradientni aniqlang:** $$ k = -\frac{a}{b} > 0 $$ (ijobiy). 4. **Grafikni chizib, x-intersept va y-interseptni bog'ing.** Chiziq ijobiy gradientga ega, birinchi kvadrantga qarab yuqoriga ko'tariladi. Bu qadamlar orqali to'g'ri chiziqning to'g'ri eskizini olishingiz mumkin.

\( a>0 ; b<0 ; c<0 \) bo'lsa, \( a x+b y+c=0 \) to'g'ri chiziqning eskizini chizing.

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