Question

The ticket sales for a concert started at 4:00 pm. The table shows the linear

relationship between the number of tickets remaining and the number of hours
since 4:00 pm. Write an equation that represents this table. Do NOT use any
commas in your answer.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{9000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3000}-\stackrel{y1}{9000}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -6000 }{ 2 } \implies - 3000`

`\begin{array}c \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}{9000}=\stackrel{m}{- 3000}(x-\stackrel{x_1}{2}) \\\\\\ y-9000=-3000x+6000\implies {\Large \begin{array}{llll} y=-3000x+15000 \end{array}}`