Question

dada a reta r: 3x + 6y - 3 = 0 escreva a reta s paralela a reta r que passa por p (4,5)

Answer 1

$\large\boxed{\begin{array}{l}\rm r:3x+6y-3=0\\\rm m_r=-\dfrac{3}{6}=-\dfrac{1}{2}\\\\\rm s\parallel r\iff m_s=m_r=-\dfrac{1}{2}\\\rm y=y_0+m\cdot(x-x_0)\\\rm y=5-\dfrac{1}{2}\cdot(x-4)\\\\\rm y=5-\dfrac{1}{2}x+2\bullet(2)\\\\\rm 2y=10-x+4\\\rm x+2y-10-4=0\\\rm s: x+2y-14=0\end{array}}$