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

Which Equation Models The Total Profitybased On The Number Of Tickets Soldx class=

Sagot :

Answer

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

Step-by-step explanation

Variables

• x: tickets sold

,

• y: profit

Equation of a line in point-slope form

[tex]y-y_1=m(x-x_1)[/tex]

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:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

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:

[tex]\begin{gathered} m=\frac{700-300}{200-100} \\ m=\frac{400}{100} \\ m=4 \end{gathered}[/tex]

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

[tex]y-300=4(x-100)[/tex]