Martinez Davies
04/25/2024 · High School
CURRENT OBfECTive Identify y-intercept in applications Question A group of students decides to make and sell cupcakes to raise money for their after-school group. To get started, they spend \( \$ 350 \) on all the supplies they will need. After determining how many cupcakes they can make with their supplies, they are happy with the profit they will earn by selling the cupcakes for \( \$ 2.50 \) each. What is the \( y \)-intercept in this situation? Do not include units in your answer. Somy thatis incorrect. Thy again?
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Step-by-step Solution
In this scenario, we can model the situation with a linear equation where the total profit \( P \) is a function of the number of cupcakes sold \( x \).
The total profit can be expressed as:
\[
P = 2.50x - 350
\]
Here:
- \( 2.50x \) represents the revenue from selling \( x \) cupcakes at \( \$ 2.50 \) each.
- \( -350 \) represents the initial cost (the fixed cost) of supplies.
The \( y \)-intercept of this equation occurs when \( x = 0 \), which represents the situation before any cupcakes are sold. To find the \( y \)-intercept, we substitute \( x = 0 \) into the equation:
\[
P = 2.50(0) - 350 = -350
\]
Thus, the \( y \)-intercept in this situation is:
\[
-350
\]
So, the answer is \( -350 \).
Quick Answer
The \( y \)-intercept is \( -350 \).
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