Question: Lucia bought a table and some chairs at a furniture store.
The equation that models this situation is $y = 40x + 55$, where $y$ is the amount
of money she spent and $x$ is the number of chairs bought.
What does the y-intercept mean in this situation?
A. She paid $40 for each chair.
B. She paid $40 for the table.
C. She paid $55 for each chair.
D. She paid $55 for the table.
1. **State the problem:** We have the equation $$y = 40x + 55$$ where $y$ is the total amount of money spent and $x$ is the number of chairs bought.
2. **Identify the y-intercept:** The y-intercept is the value of $y$ when $x=0$. In the equation $$y = 40x + 55$$, the y-intercept is $55$.
3. **Interpret the y-intercept in context:** When $x=0$, it means Lucia bought zero chairs. The amount spent, $y$, is then $55$.
4. **Meaning:** The $55$ represents the cost of the table alone, since no chairs were bought.
5. **Conclusion:** The y-intercept means Lucia paid $55$ for the table.
**Final answer:** D. She paid $55$ for the table.