[tex]\bf \begin{array}{ccccccccc}
&&\stackrel{students}{x_1}&&\stackrel{price}{y_1}&&\stackrel{students}{x_2}&&\stackrel{price}{y_2}\\
% (a,b)
&&(~{{ 10}} &,&{{ 107}}~)
% (c,d)
&&(~{{ 15}} &,&{{ 137}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{137-107}{15-10}\implies \cfrac{30}{5}\implies \cfrac{6}{1}\implies 6[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-107=6(x-10)
\\\\\\
y-107=6x-60
\implies
y=6x+47\\\\
-------------------------------\\\\
\textit{how much will it be for }\stackrel{x}{12~students?}\qquad y=6(12)+47[/tex]
