Question

Determine a equação geral da reta que passa pelos pontos (0, - 3) e (4, 3).​

Answer 1

✅ Após resolver os cálculos, concluímos que a equação geral da reta é:

          $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf r: - 3x + 2y+ 6 = 0\:\:\:}}\end{gathered} }$

Sejam os pontos:

                 $\Large\begin{cases} A(0, -3)\\B(4, 3)\end{cases}$

A equação geral  de uma reta no plano cartesiano pode ser escrita na forma:

        $\Large\displaystyle\begin{gathered} Ax+ By +C = 0,\:\:\textrm{com}\:A\neq0\:e\:B\neq0\end{gathered}$

Para determinar a equação geral da reta no plano cartesiano, devemos fazer:

      $\Large\displaystyle\begin{gathered} y - y_{A} = m_{r}\cdot(x - x_{A})\end{gathered}$

      $\Large\displaystyle\begin{gathered} y - y_{A} = \tan\theta\cdot(x- x_{A})\end{gathered}$

      $\Large\displaystyle\begin{gathered} y- y_{A} = \frac{\sin\theta}{\cos\theta}\cdot(x - x_{A})\end{gathered}$

      $\Large\displaystyle\text{ \begin{gathered} y - y_{A} = \frac{y_{B} - y_{A}}{x_{B} - x_{A}}\cdot(x - x_{A})\end{gathered} }$

 $\Large\displaystyle\begin{gathered} y- (-3) = \frac{3 - (-3)}{4 - 0}\cdot(x - 0)\end{gathered}$

          $\Large\displaystyle\begin{gathered} y + 3 = \frac{3 + 3}{4}\cdot x\end{gathered}$

          $\Large\displaystyle\begin{gathered} y + 3 = \frac{6}{4}x\end{gathered}$

          $\Large\displaystyle\begin{gathered} 4(y + 3) = 6x\end{gathered}$

        $\Large\displaystyle\begin{gathered} 4y + 12 - 6x = 0\end{gathered}$

    $\Large\displaystyle\begin{gathered} -6x + 4y + 12 = 0\end{gathered}$

       $\Large\displaystyle\begin{gathered} -3x + 2y + 6 = 0\end{gathered}$

✅ Portanto, a equação geral da reta é:

    $\Large\displaystyle\begin{gathered} r: -3x + 2y + 6 = 0\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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$\Large\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Observe \:o\:Gr\acute{a}fico!!\:\:\:}}}\end{gathered} }$