Answer:
The number of hours = x
Total number of customers served = y
The total number of cusomers at x hours can be modeled using the equation of a line
Let us pick the data for the first two rows on the table. (Note that any two rows can be picked since it is linear)
[tex]x_1=1,y_1=135,x_2=2,y_2=\text{ 195}[/tex]
The equation of a line is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope and given by the formula:} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{195-135}{2-1} \\ m\text{ = 60} \end{gathered}[/tex][tex]\begin{gathered} \text{Substitute x}_1,y_1,\text{ and m into the equation of the line:} \\ y\text{ - 135 = 60 (x - 1)} \\ y\text{ - 135 = 60x - 60} \\ y\text{ = 60x - 60 + 135} \\ y\text{ = 60x }+75 \end{gathered}[/tex]
The equation that will represent the total number of customers served x hours after the shift began is y = 60x + 75
