Question
Question 6 of 10
The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes.
On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer
matches the graph you drew, including the correct axis labels.
The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes.
On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer
matches the graph you drew, including the correct axis labels.
Answers
GPT-4o mini
To graph the cost function \( c(x) = 3x + 2 \), you'll follow these steps:
1. **Identify the function parameters:**
- This is a linear function where:
- The slope (m) = 3
- The y-intercept (b) = 2
2. **Plot the y-intercept:**
- Start at the point (0, 2) on the graph, which is where the taxi ride starts, even if no time has passed.
3. **Use the slope to plot additional points:**
- From the intercept (0, 2), you can use the slope to find another point.
- Since the slope is 3, you can go up 3 units in the y-direction and 1 unit in the x-direction. This gives you the point (1, 5).
4. **Additional points from the slope:**
- From (1, 5), if you move another minute (x = 2), you’ll go up 3 more units to (2, 8).
- You can continue this for additional values such as (3, 11) and (4, 14).
5. **Draw the line:**
- Connect the points you’ve plotted with a straight line. This will be your graph of the function \( c(x) = 3x + 2 \).
6. **Label your axes:**
- The x-axis should be labeled as "Time (minutes)".
- The y-axis should be labeled as "Cost ($)" for the cost incurred based on the ride duration.
7. **Determine the characteristics of the graph:**
- The line will rise steeply because of the slope of 3, indicating that the cost increases significantly with each additional minute.
If you had multiple choice answers, look for a graph that features:
- A straight line starting at (0, 2),
- It increases steeply reflecting a slope of 3,
- Correct axis labels for time and cost.
You now have everything you need to find the correct graph among provided options!
1. **Identify the function parameters:**
- This is a linear function where:
- The slope (m) = 3
- The y-intercept (b) = 2
2. **Plot the y-intercept:**
- Start at the point (0, 2) on the graph, which is where the taxi ride starts, even if no time has passed.
3. **Use the slope to plot additional points:**
- From the intercept (0, 2), you can use the slope to find another point.
- Since the slope is 3, you can go up 3 units in the y-direction and 1 unit in the x-direction. This gives you the point (1, 5).
4. **Additional points from the slope:**
- From (1, 5), if you move another minute (x = 2), you’ll go up 3 more units to (2, 8).
- You can continue this for additional values such as (3, 11) and (4, 14).
5. **Draw the line:**
- Connect the points you’ve plotted with a straight line. This will be your graph of the function \( c(x) = 3x + 2 \).
6. **Label your axes:**
- The x-axis should be labeled as "Time (minutes)".
- The y-axis should be labeled as "Cost ($)" for the cost incurred based on the ride duration.
7. **Determine the characteristics of the graph:**
- The line will rise steeply because of the slope of 3, indicating that the cost increases significantly with each additional minute.
If you had multiple choice answers, look for a graph that features:
- A straight line starting at (0, 2),
- It increases steeply reflecting a slope of 3,
- Correct axis labels for time and cost.
You now have everything you need to find the correct graph among provided options!