Question

Obtenha a equação reduzida da reta que passa em (-1 , 3) e é perpendicular a 2x -5y +7=0.

Answer 1

$\boxed{\begin{array}{l}\sf sejam~as~retas:\\\begin{cases}\sf r: y=m_rx+n_r\\\sf s: y=m_sx+n_s\end{cases}\\\sf r\perp s\Longleftrightarrow m_r\cdot m_s=-1\\\sf ou ~seja,duas~retas~s\tilde ao~perpendiculares\\\sf quando~o~produto~dos~coeficientes~angulares\\\sf\acute e~igual~a~-1.\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf r:2x-5y+7=0\implies y=\dfrac{2}{5}x+\dfrac{7}{5}\\\sf s: y= m_sx+n_s\end{cases}\\\sf m_r\cdot m_s=-1\\\sf \dfrac{2}{5}\cdot m_s=-1\\\sf m_s=-\dfrac{5}{2}\\\sf y=y_0+m(x-x_0)\\\sf y=3-\dfrac{5}{2}(x-(-1))\\\sf y=3-\dfrac{5}{2}(x+1)\\\sf y=3-\dfrac{5}{2}x-\dfrac{5}{2}\\\sf s: y=\dfrac{5}{2}x+\dfrac{1}{2}\end{array}}$