The Cost, $c(x$\], For A Taxi Ride Is Given By $c(x) = 2x + 4.00$, Where $x$ Is The Number Of Minutes. What Does The Slope Mean For This Situation?A. The Taxi Ride Costs \$2.00 Per Trip. B. The Taxi Ride Costs A Total Of

Mar 1, 2025 by ADMIN 223 views

The Cost of a Taxi Ride: Understanding the Slope

When it comes to calculating the cost of a taxi ride, understanding the slope of the cost function is crucial. In this article, we will delve into the world of mathematics and explore the meaning behind the slope in the context of a taxi ride. We will examine the cost function, $c(x) = 2x + 4.00$ , where $x$ represents the number of minutes, and determine what the slope signifies in this situation.

The cost function, $c(x) = 2x + 4.00$ , is a linear equation that represents the cost of a taxi ride. Here, $x$ is the number of minutes, and $c(x)$ is the cost in dollars. The equation can be broken down into two parts: the slope, $2$ , and the y-intercept, $4.00$ .

The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes. In other words, it signifies the amount of money that is added to the cost for every additional minute of the taxi ride. To put it simply, the slope tells us how much the cost increases per minute.

Let's consider an example to illustrate the meaning of the slope. Suppose we want to know the cost of a 10-minute taxi ride. We can plug in $x = 10$ into the cost function:

$c(10) = 2(10) + 4.00 = 20 + 4.00 = 24.00$

This means that the cost of a 10-minute taxi ride is $24.00. Now, let's examine the cost of a 15-minute taxi ride:

$c(15) = 2(15) + 4.00 = 30 + 4.00 = 34.00$

As we can see, the cost of the 15-minute taxi ride is $34.00, which is $10.00 more than the cost of the 10-minute taxi ride. This $10.00 increase is a direct result of the slope, $2$ , which represents the rate of change of the cost with respect to the number of minutes.

The slope, $2$ , can also be interpreted as the cost per minute. This means that for every additional minute of the taxi ride, the cost increases by $2.00. To put it simply, the slope tells us that the taxi ride costs $2.00 per minute.

In conclusion, the slope of the cost function, $c(x) = 2x + 4.00$ , represents the rate of change of the cost with respect to the number of minutes. It signifies the amount of money that is added to the cost for every additional minute of the taxi ride. The slope can also be interpreted as the cost per minute, which is $2.00. Understanding the slope is crucial in calculating the cost of a taxi ride and making informed decisions about transportation.

What does the slope mean for this situation?
Is the slope a fixed value or does it change depending on the number of minutes?
How does the slope affect the cost of a taxi ride?

A. The taxi ride costs $2.00 per minute.

B. The taxi ride costs a total of $24.00 for a 10-minute ride.

C. The taxi ride costs a total of $34.00 for a 15-minute ride.

Mathematics
Cost Function
Slope
The Cost of a Taxi Ride: A Q&A Guide

In our previous article, we explored the cost function, $c(x) = 2x + 4.00$ , and the meaning behind the slope in the context of a taxi ride. We discussed how the slope represents the rate of change of the cost with respect to the number of minutes and how it can be interpreted as the cost per minute. In this article, we will provide a Q&A guide to help you better understand the cost of a taxi ride and the slope.

Q1: What does the slope mean for this situation?

A1: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes. It signifies the amount of money that is added to the cost for every additional minute of the taxi ride.

Q2: Is the slope a fixed value or does it change depending on the number of minutes?

A2: The slope, $2$ , is a fixed value. It does not change depending on the number of minutes.

Q3: How does the slope affect the cost of a taxi ride?

A3: The slope affects the cost of a taxi ride by increasing the cost by $2.00 for every additional minute.

Q4: What is the cost per minute?

A4: The cost per minute is $2.00.

Q5: How can I calculate the cost of a taxi ride?

A5: To calculate the cost of a taxi ride, you can use the cost function, $c(x) = 2x + 4.00$ , where $x$ is the number of minutes.

Q6: What is the y-intercept in the cost function?

A6: The y-intercept in the cost function, $c(x) = 2x + 4.00$ , is $4.00. This represents the initial cost of the taxi ride.

Q7: Can I use the slope to calculate the cost of a taxi ride for a specific number of minutes?

A7: Yes, you can use the slope to calculate the cost of a taxi ride for a specific number of minutes. For example, if you want to know the cost of a 10-minute taxi ride, you can plug in $x = 10$ into the cost function: $c(10) = 2(10) + 4.00 = 20 + 4.00 = 24.00$ .

Q8: How does the slope relate to the cost of a taxi ride?

A8: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes. It signifies the amount of money that is added to the cost for every additional minute of the taxi ride.

Q9: Can I use the slope to compare the cost of different taxi rides?

A9: Yes, you can use the slope to compare the cost of different taxi rides. For example, if you want to compare the cost of a 10-minute taxi ride and a 15-minute taxi ride, you can use the slope to calculate the cost of each ride and compare the results.

Q10: What is the significance of the slope in the context of a taxi ride?

A10: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes. It signifies the amount of money that is added to the cost for every additional minute of the taxi ride. This is significant because it helps you understand how the cost of a taxi ride changes over time.

In conclusion, the slope of the cost function, $c(x) = 2x + 4.00$ , represents the rate of change of the cost with respect to the number of minutes. It signifies the amount of money that is added to the cost for every additional minute of the taxi ride. We hope this Q&A guide has helped you better understand the cost of a taxi ride and the slope.

What are some real-world applications of the slope in the context of a taxi ride?
How can the slope be used to compare the cost of different taxi rides?
What are some potential limitations of using the slope to calculate the cost of a taxi ride?

A1: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes.

A2: The slope, $2$ , is a fixed value.

A3: The slope affects the cost of a taxi ride by increasing the cost by $2.00 for every additional minute.

A4: The cost per minute is $2.00.

A5: To calculate the cost of a taxi ride, you can use the cost function, $c(x) = 2x + 4.00$ , where $x$ is the number of minutes.

A6: The y-intercept in the cost function, $c(x) = 2x + 4.00$ , is $4.00.

A7: Yes, you can use the slope to calculate the cost of a taxi ride for a specific number of minutes.

A8: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes.

A9: Yes, you can use the slope to compare the cost of different taxi rides.

A10: The slope, $2$ , represents the rate of change of the cost with respect to the number of minutes.