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nataly862011 [7]
3 years ago
9

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

Mathematics
1 answer:
Anestetic [448]3 years ago
7 0
\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
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The unit rates grater than the graph's from small to large are:

y=\frac{13}{6}x             y= \frac{11}{5}x          y = \frac{21}{9}x          y = \frac{19}{8}x

m=\frac{13}{6}              m= \frac{11}{5}           m = \frac{21}{9}            m = \frac{19}{8}

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