[tex]\bf \begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{miles}&\stackrel{y}{cost(\$)}\\ \cline{1-2} 3&9.5\\ 7&15\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{3}~,~\stackrel{y_1}{9.5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{15}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{15}-\stackrel{y1}{9.5}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{3}}}\implies \cfrac{5.5}{4}\implies \cfrac{1.375}{1}\implies 1.375[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9.5}=\stackrel{m}{1.375}(x-\stackrel{x_1}{3}) \\\\\\ y-9.5=1.375x-4.125\implies y = 1.375x+5.375[/tex]
B)
in the equation, we have a slope of 1.375 and a y-intercept of 5.375 or namely the point at (0 , 5.375). Let's recall that the y-intercept occurs when the x = 0, namely when "x" is 0 or at 0 miles travelled, we have a cost of $5.375, that means that the taxi driver has a start service fee of $5.375, namely just by getting in the cab you owe that much, and any mile(x) you after that, is an extra charge.
C)
how much is that extra charge from B)? well, after you pay the $5.375 service fee, if you go a mile x = 1, you owe 1.375(1), after going 2 miles x = 2, you owe 1.375(2) and so on, the slope means how much it costs per mile for the trip, after the service fee.
