Answer
$y = -\frac12x -\frac{11}2$
Work Step by Step
We are told to find the equation of the line that satisfies the following conditions:
Passes through the point $(1,-6)$, and parallel to the line $x + 2y = 6$
To find the equation of the line we must find the slope and then use point slope form: $y−y_1=m(x−x_1)$
First solve the given equation for $y$:
$x + 2y = 6$
$2y = -x + 6$
$y = -\frac{1}{2}x + 3$
Since the lines are parallel they have the same slope, so the slope of our equation is $m = -\frac12$
$y− (-6)=-\frac12(x− 1)$
$y=-\frac12x +\frac12 -6$
$y = -\frac12x -\frac{11}2$