## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$y-2=-1(x+3)$
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}