Question

It costs $107 for 10 students and $137 for 15 students. How much does it cost for 12 students?

Answer 1

$\bf \begin{array}{ccccccccc} &&\stackrel{students}{x_1}&&\stackrel{price}{y_1}&&\stackrel{students}{x_2}&&\stackrel{price}{y_2}\\ % (a,b) &&(~{{ 10}} &,&{{ 107}}~) % (c,d) &&(~{{ 15}} &,&{{ 137}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{137-107}{15-10}\implies \cfrac{30}{5}\implies \cfrac{6}{1}\implies 6$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-107=6(x-10) \\\\\\ y-107=6x-60 \implies y=6x+47\\\\ -------------------------------\\\\ \textit{how much will it be for }\stackrel{x}{12~students?}\qquad y=6(12)+47$