Question

O coeficiente linear da reta que passa pelos pontos A (-1, -6) e B (2, 3) é:

a) 3
b) 1
c) 1/3
d) -1/3
e) -3

Answer 1

✅ Após resolver os cálculos, concluímos que o coeficiente angular da reta que passa pelos referidos pontos "A" e "B" é:

            $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf m_{r} = 3\:\:\:}}\end{gathered} }$

Portanto, a opção correta é:

     $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf Alternativa\:A\:\:\:}}\end{gathered} }$

Sejam os pontos:

              $\Large\begin{cases} A(-1,-6)\\B(2, 3)\end{cases}$

Sabemos que o coeficiente angular da reta é numericamente igual à tangente do ângulo de inclinação, ou seja:

         $\Large\displaystyle\begin{gathered} m_{r} = \tan\theta\end{gathered}$

                 $\Large\displaystyle\begin{gathered} = \frac{\sin\theta}{\cos\theta}\end{gathered}$

                 $\Large\displaystyle\text{ \begin{gathered} = \frac{y_{B} - y_{A}}{x_{B} - x_{A}}\end{gathered} }$

                 $\Large\displaystyle\begin{gathered} = \frac{3 - (-6)}{2 - (-1)}\end{gathered}$

                 $\Large\displaystyle\begin{gathered} = \frac{3 + 6}{2 + 1}\end{gathered}$

                 $\Large\displaystyle\begin{gathered} = \frac{9}{3}\end{gathered}$

                 $\Large\displaystyle\begin{gathered} = 3\end{gathered}$

✅ Portanto, o coeficiente angular é:

            $\Large\displaystyle\begin{gathered} m_{r} = 3\end{gathered}$

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

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