Answer
$y=x-32$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept.
(3) Parallel lines have equal slopes.
(4) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Write $x+y=18$ in slope-intercept form:
$x+y=18
\\y=18-x
\\y=-x+18$
This means the equation $x+y=18$ is equivalent to $y=-x+18$.
The line is perpendicular to $y=-x+18$. Since the slope of this line is $-1$, then the slope of the line perpendicular to it is the negative reciprocal of $-1$, which is $1$.
Using the given point on the line $(0, -32)$ (which is the y-intercept) and the slope $1$, the equation of the line in slope-intercept form is:
$y=x+(-32)
\\y=x-32$
