parallel lines have the same exact slope hmmm what's the slope of y = 2/3x-7 anyway? well, low and behold, is already in slope-intercept form, therefore
[tex] \bf \stackrel{\textit{slope-intercept form}}{y=\stackrel{slope}{\cfrac{2}{3}}x-7} [/tex].
so we're really looking for the equation of a line whose slope is 2/3, and runs through 3, -1.
[tex] \bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})~\hspace{7em}
slope = m\implies \cfrac{2}{3}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-1)=\cfrac{2}{3}(x-3)
\\\\\\
y+1=\cfrac{2}{3}x-2\implies y=\cfrac{2}{3}x-3 [/tex]
