Question

Calcule o coeficiente angular e a equação das retas Y1 e Y2
A reta Y1 que passa pelos pontos (1,8) e (-2,1) e a reta Y2, que é perpendicular à reta Y1 e passa pelo ponto (-1, 2).

Answer 1

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$\boxed{\sf m_1=\dfrac{1-8}{-2-1}=\dfrac{-7}{-3}=\dfrac{7}{3}}\\\sf y_1=1+\dfrac{7}{3}\cdot(x-(-2))\\\sf y_1=1+\dfrac{7}{3}\cdot(x+2)\\\sf y_1=1+\dfrac{7}{3}x+\dfrac{14}{3}\\\boxed{\sf y_1=\dfrac{7}{3}x+\dfrac{17}{4}}\\\sf y_1\perp y_2\Longleftrightarrow m_1\cdot m_2=-1\\\sf \dfrac{7}{3}\cdot m_2=-1\\\sf 7m_2=-3\\\boxed{\sf m_2=-\dfrac{3}{7}}\\\sf y_2=2-\dfrac{3}{7}\cdot(x-(-2))\\\sf y_2=2-\dfrac{3}{7}\cdot(x+2)\\\sf y_2=2-\dfrac{3}{7}x-\dfrac{6}{7}\\\boxed{\sf y_2=-\dfrac{3}{7}x+\dfrac{8}{7}}$