Question

Which equation models the total profit,y,based on the number of tickets sold,x?

Answer 1

D. y - 300 = 4(x - 100)

Explanation

Variables

• x: tickets sold

,

• y: profit

Equation of a line in point-slope form

`y-y_1=m(x-x_1)`

where m is the slope and (x₁, y₁) is a point on the line.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

`m=(y_2-y_1)/(x_2-x_1)`

This line passes through the points (100, 300), that is, when 100 tickets are sold, the club had $300 in profit, and the point (200, 700). Then, its slope is:

`\begin{gathered} m=(700-300)/(200-100) \\ m=(400)/(100) \\ m=4 \end{gathered}`

Substituting into the general equation with m = 4 and the point (100, 300), we get the next equation of the line:

`y-300=4(x-100)`