Question
A dance studio in Charleston, South Carolina, charges a one-time registration fee of $53.75 and $43 per month for classes. (6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Part A: What is the equation for the cost of dance classes if y
is the total cost (in dollars) for joining for a certain number of months,x
y=
Part B: Graph the equation using Desmos. (Link to Desmos)
Part C: Determine the key feature of the function
x-intercept
y-intercept
slope
domain In the context of the problem
range in the context of the problem
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Part A: What is the equation for the cost of dance classes if y
is the total cost (in dollars) for joining for a certain number of months,x
y=
Part B: Graph the equation using Desmos. (Link to Desmos)
Part C: Determine the key feature of the function
x-intercept
y-intercept
slope
domain In the context of the problem
range in the context of the problem
Answers
GPT-4o mini
To solve this problem, let's break it down into its parts.
### Part A: Cost Equation
The total cost \( y \) of joining the dance studio can be modeled by the equation:
\[
y = 43x + 53.75
\]
Where:
- \( 43 \) represents the cost per month,
- \( x \) represents the number of months of classes,
- \( 53.75 \) is the one-time registration fee.
### Part B: Graphing
To graph the equation, you will need to use Desmos. Here is a brief guide to how you can do that:
1. Go to [Desmos.com](https://www.desmos.com/calculator).
2. Input the equation \( y = 43x + 53.75 \) into a new expression line.
3. You will be able to see the graph of the equation immediately.
### Part C: Key Features of the Function
Now let’s determine the key features of the linear function:
1. **x-intercept**: This is the point where the graph crosses the x-axis (where \( y = 0 \)).
- Setting \( y = 0 \):
\[
0 = 43x + 53.75 \implies x = -\frac{53.75}{43} \approx -1.25
\]
So the x-intercept is approximately \((-1.25, 0)\).
2. **y-intercept**: This is the point where the graph crosses the y-axis (where \( x = 0 \)).
- Setting \( x = 0 \):
\[
y = 43(0) + 53.75 = 53.75
\]
So the y-intercept is \((0, 53.75)\).
3. **Slope**: This represents the rate of change; here, the slope is the coefficient of \( x \).
\[
\text{slope} = 43
\]
4. **Domain in the context of the problem**: The domain represents the number of months. Since you can't have negative months:
\[
\text{Domain: } x \geq 0
\]
5. **Range in the context of the problem**: The range represents the total cost. Since the cost is always positive and starts from the registration fee:
\[
\text{Range: } y \geq 53.75
\]
### Summary of Key Features
- **x-intercept**: Approximately \((-1.25, 0)\)
- **y-intercept**: \((0, 53.75)\)
- **slope**: 43
- **domain**: \( x \geq 0 \)
- **range**: \( y \geq 53.75 \)
Feel free to ask if you need further clarification or assistance!
### Part A: Cost Equation
The total cost \( y \) of joining the dance studio can be modeled by the equation:
\[
y = 43x + 53.75
\]
Where:
- \( 43 \) represents the cost per month,
- \( x \) represents the number of months of classes,
- \( 53.75 \) is the one-time registration fee.
### Part B: Graphing
To graph the equation, you will need to use Desmos. Here is a brief guide to how you can do that:
1. Go to [Desmos.com](https://www.desmos.com/calculator).
2. Input the equation \( y = 43x + 53.75 \) into a new expression line.
3. You will be able to see the graph of the equation immediately.
### Part C: Key Features of the Function
Now let’s determine the key features of the linear function:
1. **x-intercept**: This is the point where the graph crosses the x-axis (where \( y = 0 \)).
- Setting \( y = 0 \):
\[
0 = 43x + 53.75 \implies x = -\frac{53.75}{43} \approx -1.25
\]
So the x-intercept is approximately \((-1.25, 0)\).
2. **y-intercept**: This is the point where the graph crosses the y-axis (where \( x = 0 \)).
- Setting \( x = 0 \):
\[
y = 43(0) + 53.75 = 53.75
\]
So the y-intercept is \((0, 53.75)\).
3. **Slope**: This represents the rate of change; here, the slope is the coefficient of \( x \).
\[
\text{slope} = 43
\]
4. **Domain in the context of the problem**: The domain represents the number of months. Since you can't have negative months:
\[
\text{Domain: } x \geq 0
\]
5. **Range in the context of the problem**: The range represents the total cost. Since the cost is always positive and starts from the registration fee:
\[
\text{Range: } y \geq 53.75
\]
### Summary of Key Features
- **x-intercept**: Approximately \((-1.25, 0)\)
- **y-intercept**: \((0, 53.75)\)
- **slope**: 43
- **domain**: \( x \geq 0 \)
- **range**: \( y \geq 53.75 \)
Feel free to ask if you need further clarification or assistance!