(i) Equation : y = 6.25x + 65
(ii) Price of each ticket : $6.25
(iii) Money originally in the box : $65
Explanation:
Here from table, identify the coordinates given.
Coordinates:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{146.25-108.75}{13-7} = 6.25[/tex]
Slope is also the price of each ticket which is $6.25
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\rightarrow \sf y - 108.75 = 6.25(x - 7)[/tex]
[tex]\rightarrow \sf y - 108.75 = 6.25x - 43.75[/tex]
[tex]\rightarrow \sf y = 6.25x - 43.75 + 108.75[/tex]
[tex]\rightarrow \sf y = 6.25x +65[/tex]
To find the amount of money in the box originally, insert x which represents number of tickets sold as 0.
Originally amount of money:
[tex]\rightarrow \sf y = 6.25(0) +65[/tex]
[tex]\rightarrow \sf y = 65[/tex]
Hence, there were $65 in the box before any tickets were sold.
