Answer
$y-2=-1(x+3)$
Work Step by Step
Using the properties of equality, the given linear equation, $
x+y=7
$ is equivalent to
\begin{array}{l}
y=-x+7
.\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 parallel lines have the same slope, then the needed linear equation has the same slope and it passes through the given point $(
-3,2
)$. 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, then the equation of the needed line is
\begin{array}{l}
y-2=-1(x-(-3))
\\\\
y-2=-1(x+3)
.\end{array}
