well, a line parallel to that one on the graph, will have the same exact slope, wait just a second, what the dickens is the slope of that one on the graph anyway?
well, let's pick two points off of it hmmmmm let's use those given ones, (-3,3) and (-2,1),
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -3 &,& 3~)
% (c,d)
&&(~ -2 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-3}{-2-(-3)}
\\\\\\
\cfrac{1-3}{-2+3}\implies \cfrac{-2}{1}\implies -2[/tex]
alrity, so the graphed line has a slope of -2, then our parallel line will also have a slope of -2, and we also know that it passes through 4,1,
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
% (a,b)
&&(~ 4 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies -2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=-2(x-4)[/tex]
