Dylan was given a gift card for a coffee shop. Each morning, Dylan uses the card to buy one cup of coffee. Let A represent the amount money remaining on the card after buying x cups of coffee. A graph of A is shown below. Write an equation for A then state the x- intercept of the graph and determine its interpretation in the context of the problem.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Description:**

Dylan was given a gift card for a coffee shop. Each morning, Dylan uses the card to buy one cup of coffee. Let \( A \) represent the amount of money remaining on the card after buying \( x \) cups of coffee. A graph of \( A \) is shown below. Write an equation for \( A \) then state the \( x \)-intercept of the graph and determine its interpretation in the context of the problem.

**Graph Explanation:**

- **Axes:**
  - The horizontal axis (x-axis) represents the "Number of Cups of Coffee" Dylan buys, labeled from 0 to 8.
  - The vertical axis (y-axis) represents the "Amount of Money Remaining on Card," labeled from 0 to 17.

- **Line:**
  - The graph shows a dotted line with a negative slope, starting from \( (0, 15) \) and going down to approximately \( (6, 0) \).
  - The line is dotted because the domain of the function is limited to integers, reflecting that Dylan can only purchase a whole number of cups.

- **Note:**
  - Below the graph, a note mentions that the line is drawn as dotted due to the domain being restricted to integers.
Transcribed Image Text:**Problem Description:** Dylan was given a gift card for a coffee shop. Each morning, Dylan uses the card to buy one cup of coffee. Let \( A \) represent the amount of money remaining on the card after buying \( x \) cups of coffee. A graph of \( A \) is shown below. Write an equation for \( A \) then state the \( x \)-intercept of the graph and determine its interpretation in the context of the problem. **Graph Explanation:** - **Axes:** - The horizontal axis (x-axis) represents the "Number of Cups of Coffee" Dylan buys, labeled from 0 to 8. - The vertical axis (y-axis) represents the "Amount of Money Remaining on Card," labeled from 0 to 17. - **Line:** - The graph shows a dotted line with a negative slope, starting from \( (0, 15) \) and going down to approximately \( (6, 0) \). - The line is dotted because the domain of the function is limited to integers, reflecting that Dylan can only purchase a whole number of cups. - **Note:** - Below the graph, a note mentions that the line is drawn as dotted due to the domain being restricted to integers.
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