Question

Determine a equação da reta que passa por P e tem coef. angular m nos casos:

Answer 1

Olá, tudo bem?
A fórmula da equação da reta para este caso é:

$y-y_P=m(x-x_P)$

vamos usar a mesma fórmula para todas as questões okay?:

$A)P(3,7)\ e\ m=-2\\\\ y-y_p=m(x-x_p)\\ y-3=-2(x-3)\\ y-3=-2x+6\\ y=-2x+6+3\\\\ \boxed{\boxed{y=-2x+9}}$

$B)P(-1,-2)\ e\ m= \frac{1}{2}\\\\ y-y_p=m(x-x_p)\\ y+2=\frac{1}{2}\cdot(x+1)\\\\ y+2= \frac{x}{2}+ \frac{1}{2}\\\\ y= \frac{x}{2} + \frac{1}{2} -2\\\\ y= \frac{x}{2}+ \frac{1-(2\cdot2)}{2}\\\\\boxed{\boxed{y= \frac{x-3}{2}}}\\\\\\ C)P(0,4)\ e\ m=\frac{1}{2}\\\\ y-y_p=m(x-x_p)\\\\ y-4=\frac{1}{2}\cdot(x-0)\\\\ y-4=\frac{x}{2}-0\\\\y= \frac{x}{2}+4\\\\ \boxed{\boxed{y= \frac{x+8}{2} }}$


$D)P(-2,1)\ e\ m=\frac{-1}{5}\\\\ y-y_p=m(x-x_p)\\\\ y-1=\frac{-1}{5}\cdot(x+2)\\\\ y-1= \frac{-x}{5}- \frac{2}{5} \\\\ y=- \frac{x}{5}- \frac{2+(5\cdot1)}{5}\\\\ y= \frac{-x}{5}- \frac{7}{5} \\\\\\ \boxed{\boxed{y= \frac{-x-7}{5}}}$