Question

Encontre a forma geral da equação da reta que passa pelos pontos:
a) A ( 0 , 2 ) e B ( 2 , 3 ) b) C ( -1 , 2 ) e D ( -2 , 5 )
Me ajudem

Answer 1

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☞ a) y - (x/2) - 2 = 0; b) y + 3x + 1 = 0  ✅

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O~PASSO{-}A{-}PASSO~~~}}$✍

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☔ Oi, Ana. Inicialmente  lembremos da equação geral da reta:

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$\LARGE\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf ax + by + c = 0}&\\&&\\\end{array}}}}}$

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$\text{\pink{ \Longrightarrow }~\Large\sf\orange{\sf a, b \& c}}$ sendo coeficientes.

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☔ A forma mais prática para encontrarmos esta equação, dados dois pontos, é:

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1. Encontrar o coeficiente angular m da reta;
2. Utilizar m e um dos pontos na mesma equação de m.

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$\Large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}}&\\&&\\\end{array}}}}}$

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Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\blue{\sf\Large~1.~\begin{cases}\sf~~m = \dfrac{3 - 2}{2 - 0}\\\\ \text{ ~~\boxed{\sf m = \dfrac{1}{2}} } \end{cases}}$

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$\blue{\sf\Large~2.~\begin{cases}\sf~~\dfrac{1}{2} = \dfrac{y - 2}{x - 0}\\\\ \sf~~\dfrac{x}{2} = y - 2\\\\ \text{ ~~\boxed{\sf y - \dfrac{x}{2} - 2 = 0} } \end{cases}}$

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$\LARGE\green{\boxed{\rm~~~\red{ A)}~\gray{y - \dfrac{x}{2} - 2}~\pink{=}~\blue{ 0 }~~~}}$ ✅

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\blue{\sf\Large~1.~\begin{cases}\sf~~m = \dfrac{5 - 2}{-2 - (-1)}\\\\ \sf~~m = \dfrac{3}{-1}\\\\ ~~\boxed{\sf m = -3} \end{cases}}$

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$\blue{\sf\Large~2.~\begin{cases}\sf~~-3 = \dfrac{y - 2}{x - (-1)}\\\\ \sf~~-3x - 3 = y - 2\\\\ ~~\boxed{\sf y + 3x + 1 = 0} \end{cases}}$

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$\LARGE\green{\boxed{\rm~~~\red{ B)}~\gray{y + 3x + 1}~\pink{=}~\blue{ 0 }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

☔ Exercício Semelhante:

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✈ https://brainly.com.br/tarefa/38232703;

$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\Large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$