so we know it passes through 5,2, and has the same y-intercept as y = 3x -9.... hmmmm [tex]\bf y=\stackrel{slope}{3}x\stackrel{y-intercept}{-9}[/tex].
so this one has a y-intercept at -9, therefore this line must have the same y-intercept... let's say it has a slope of "m".
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
% (a,b)
&&(~{{ 5}} &,&{{ 2}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=m(x-5)\implies y-2=mx-5m
\\\\\\
y=mx-5m+2\implies y=\stackrel{slope}{m}x\stackrel{y-intercept}{-5m+2}[/tex]
so, this one has a y-intercept of "-5m+2", which we know is the same as the other equation's, therefore -5m+2 = -9.
[tex]\bf -5m+2 = -9\implies -5m=-11\implies m=\cfrac{-11}{-5}\implies m=\cfrac{11}{5}\\\\
-------------------------------\\\\
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=m(x-5)\implies y-2=\cfrac{11}{5}(x-5)[/tex]
