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A corporate team-building event costs $\$23$ , plus an additional $\$5$ per attendee. Is the total cost directly proportional to the number of attendees? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Write a linear function: word problems

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Q. A corporate team-building event costs

\$23

, plus an additional

\$5

per attendee. Is the total cost directly proportional to the number of attendees?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Identify Components: Identify the components of the cost equation. $\newline$ The total cost for the event is made up of a fixed cost and a variable cost that depends on the number of attendees.
Write Equation: Write the equation for the total cost. $\newline$ Total cost = Fixed cost + (Cost per attendee $\times$ Number of attendees) $\newline$ Let $C$ be the total cost and $n$ be the number of attendees. $\newline$ $C = 23 + 5n$
Analyze Proportionality: Analyze if the cost is directly proportional to the number of attendees. Direct proportionality means that as one quantity increases, the other quantity increases at a constant rate. Here, the cost per attendee is constant ( $5), but there is also a fixed cost ($ $23$ ) that does not change with the number of attendees.
Consider Fixed Cost: Determine if the presence of the fixed cost affects direct proportionality. $\newline$ Since there is a fixed cost, the total cost is not solely dependent on the number of attendees. This means the relationship is not a direct proportion because of the additional fixed cost.

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