Answer
$y=x+27$
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 $x-y=6$ in slope-intercept form:
$x-y=6
\\-y=6-x
\\-1(-y)=-1(6-x)
\\y=-6+x
\\y=x-6$
This means the equation $x-y=6$ is equivalent to $y=x-6$.
The line is parallel to $y=x-6$. Since the slope of this line is $1$, then the slope of the line parallel to it is also $1$.
Using the given point on the line $(0, 27)$ (which is the y-intercept) and the slope $1$, the equation of the line in point-slope form is:
$y=x+27$
