Linear Equation from Party Cost Graph: Fixed Cost and Per-Guest Rate

Published on November 9, 2026

Word-Problem

Write a linear equation modeling total party cost from a graph showing a fixed room rental fee and a per-guest charge. Read the y-intercept as the fixed cost and compute the slope from two points on the line to get C = 12x + 40.

Question

Answer

Step 1: Find the fixed cost (y-intercept).
The line crosses the vertical axis at $40, so the fixed cost to rent the room is $40.

Step 2: Find the cost per guest (slope).
The line passes through

. Using the rate of change between

and

Step 3: Write the linear model.
Let

be the number of guests and

the total cost:

Final answer:

, where the fixed cost is $40 and each guest adds $12.

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