Answer
$y-2=1(x+4)$
Work Step by Step
Using the properties of equality, the given linear equation, $
x+y=6
$ is equivalent to
\begin{array}{l}
y=-x+6
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
-1
$. Since perpendicular lines have negative reciprocal slopes, then the needed linear equation has slope equal to $
1
$. Since it also passes through the given point $(
-4,2
)$, then using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, the equation of the needed line is
\begin{array}{l}
y-2=1(x-(-4))
\\\\
y-2=1(x+4)
.\end{array}
