Question
Dot next to number shows a point on the board. The graph shows the cost to rent a surfboard at a local shop. Use the graph to answer the following questions:
Check the appropriate box:
Independent variable:
Cost Time
Dependent variable:
cost Time
(2 points)
Y axis
Cost (dollars)
40
35
30
25
20
15
10
5
Is the relationship between the x - and y-values shown in the graph additive or multiplicative? (circle one)
(1 point)
Write the equation:
X axis
Amount of Time (hours)
1 1/2
2
3
4
5
6
Check the appropriate box:
Independent variable:
Cost Time
Dependent variable:
cost Time
(2 points)
Y axis
Cost (dollars)
40
35
30
25
20
15
10
5
Is the relationship between the x - and y-values shown in the graph additive or multiplicative? (circle one)
(1 point)
Write the equation:
X axis
Amount of Time (hours)
1 1/2
2
3
4
5
6
Answers
GPT-4o mini
To answer your questions based on the graph description you provided, I'll proceed as follows:
### 1. Identifying Independent and Dependent Variables:
- **Independent Variable**: This is the variable that you can change or control, in this case, the amount of time (in hours) spent renting the surfboard.
- **Dependent Variable**: This is the variable that depends on the independent variable, which is the cost of renting the surfboard.
Therefore, you would check:
- **Independent variable**: Time
- **Dependent variable**: Cost
### 2. Relationship Type:
To determine if the relationship between the x-values (time) and y-values (cost) is additive or multiplicative, we look at whether the cost changes by a constant amount for each additional hour (additive) or if it is multiplied by a constant factor for each additional hour (multiplicative).
Given that rental costs typically depend on a fixed rate applied per hour, it is likely to be a **multiplicative relationship**. Thus, you can circle **multiplicative**.
### 3. Writing the Equation:
To write the equation, we generally use the form:
\[ \text{Cost} = \text{Rate} \times \text{Time} \]
If we assume (for example) that the cost to rent a surfboard per hour is $10, the equation would be:
\[ \text{Cost} = 10 \times \text{Time} \]
You would need to replace the "10" with the actual cost per hour if you have that information from the graph.
---
Based on the points above, you should fill out your responses as follows:
1. Independent variable: **Time**
- Dependent variable: **Cost**
2. Relationship: **Multiplicative**
3. Equation: **Cost = 10 * Time** (or whatever the cost per hour is according to the graph data).
### 1. Identifying Independent and Dependent Variables:
- **Independent Variable**: This is the variable that you can change or control, in this case, the amount of time (in hours) spent renting the surfboard.
- **Dependent Variable**: This is the variable that depends on the independent variable, which is the cost of renting the surfboard.
Therefore, you would check:
- **Independent variable**: Time
- **Dependent variable**: Cost
### 2. Relationship Type:
To determine if the relationship between the x-values (time) and y-values (cost) is additive or multiplicative, we look at whether the cost changes by a constant amount for each additional hour (additive) or if it is multiplied by a constant factor for each additional hour (multiplicative).
Given that rental costs typically depend on a fixed rate applied per hour, it is likely to be a **multiplicative relationship**. Thus, you can circle **multiplicative**.
### 3. Writing the Equation:
To write the equation, we generally use the form:
\[ \text{Cost} = \text{Rate} \times \text{Time} \]
If we assume (for example) that the cost to rent a surfboard per hour is $10, the equation would be:
\[ \text{Cost} = 10 \times \text{Time} \]
You would need to replace the "10" with the actual cost per hour if you have that information from the graph.
---
Based on the points above, you should fill out your responses as follows:
1. Independent variable: **Time**
- Dependent variable: **Cost**
2. Relationship: **Multiplicative**
3. Equation: **Cost = 10 * Time** (or whatever the cost per hour is according to the graph data).