## Calculus 8th Edition

$y = -\frac12x -\frac{11}2$
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 $m = -\frac12$ $y− (-6)=-\frac12(x− 1)$ $y=-\frac12x +\frac12 -6$ $y = -\frac12x -\frac{11}2$