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Answer :
Answer:
Step-by-step explanation:
que5)ans:
Let's break down both parts of your question.
### Part 1: Line Passing Through (0, 5) and Proportional Relationship
To determine if a line passing through the point (0,5) represents a proportional relationship, we need to know that a proportional relationship between two variables is one where the ratio between the two variables is constant.
In a graph, a line represents a proportional relationship if it passes through the origin (0,0) and has a constant slope. The point (0, 5) is not the origin, meaning that the line does not go through (0, 0). This suggests that the relationship is **not proportional** because in a proportional relationship, the graph should start at the origin, and a constant ratio should exist between the two variables.
So, the line passing through (0,5) **does not represent a proportional relationship** because it does not pass through the origin.
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### Part 2: Melanie, Rosi, and Carlos Buying Shells
Melanie, Rosi, and Carlos buy shells at different quantities and prices, and we are asked to determine if there is a proportional relationship between the number of shells and the cost.
#### Data:
- Melanie: 2 shells for $0.80
- Rosi: 3 shells for $1.20
- Carlos: 4 shells for $1.60
We can check for proportionality by calculating the cost per shell for each person and seeing if it is the same for everyone.
1. **Melanie's price per shell**:
\[
\frac{0.80}{2} = 0.40 \, \text{per shell}
\]
2. **Rosi's price per shell**:
\[
\frac{1.20}{3} = 0.40 \, \text{per shell}
\]
3. **Carlos's price per shell**:
\[
\frac{1.60}{4} = 0.40 \, \text{per shell}
\]
Since the price per shell is the same for all three people (0.40 per shell), this shows that the cost and the number of shells are **proportional**.
#### Constant of Proportionality:
The constant of proportionality is the price per shell, which is **0.40**. This means that for every shell bought, the cost increases by $0.40.
#### Graph:
On a graph, this would be a straight line starting at the origin (0,0) with a slope of 0.40, showing that for each additional shell, the total cost increases by $0.40.
In conclusion, there **is a proportional relationship** between the cost and the number of shells, and the constant of proportionality is **0.40**, meaning each shell costs $0.40.
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