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

by ADMIN 216 views

The Cost of a Taxi Ride: Graphing and Analysis

The cost of a taxi ride is a common concern for many people, especially when traveling to unfamiliar areas. In this article, we will explore the cost function of a taxi ride, which is given by the equation { c(x) = 3x + 2.00 $}$, where { x $}$ represents the number of minutes. We will graph this function on a piece of paper and analyze the results to determine which answer matches the given equation.

Understanding the Cost Function

The cost function { c(x) = 3x + 2.00 $}$ represents the total cost of a taxi ride in dollars, where { x $}$ is the number of minutes. This means that for every minute you ride the taxi, the cost increases by { 3 $}$ dollars. The constant term { 2.00 $}$ represents the initial cost of the taxi ride, which is { 2.00 $}$ dollars.

Graphing the Cost Function

To graph the cost function, we need to plot the points on a coordinate plane. We can start by finding the x-intercept, which is the point where the cost is zero. To find the x-intercept, we set { c(x) = 0 $}$ and solve for { x $}$.

{ 0 = 3x + 2.00 $}$

Subtracting { 2.00 $}$ from both sides gives us:

{ -2.00 = 3x $}$

Dividing both sides by { 3 $}$ gives us:

{ x = -\frac{2.00}{3} $}$

So, the x-intercept is { -\frac{2.00}{3} $}$ minutes.

Next, we need to find the y-intercept, which is the point where the cost is zero. To find the y-intercept, we set { x = 0 $}$ and solve for { c(x) $}$.

{ c(0) = 3(0) + 2.00 $}$

Simplifying the equation gives us:

{ c(0) = 2.00 $}$

So, the y-intercept is { 2.00 $}$ dollars.

Now that we have the x-intercept and y-intercept, we can plot the points on a coordinate plane. We can start by plotting the x-intercept, which is { -\frac{2.00}{3} $}$ minutes. We can then plot the y-intercept, which is { 2.00 $}$ dollars.

Analyzing the Graph

The graph of the cost function is a straight line with a positive slope. This means that the cost of the taxi ride increases as the number of minutes increases. The y-intercept represents the initial cost of the taxi ride, which is { 2.00 $}$ dollars.

Determining the Answer

Based on the graph, we can determine which answer matches the given equation. The answer should have a positive slope and a y-intercept of { 2.00 $}$ dollars.

In conclusion, the cost function of a taxi ride is given by the equation { c(x) = 3x + 2.00 $}$, where { x $}$ represents the number of minutes. We graphed this function on a piece of paper and analyzed the results to determine which answer matches the given equation. The answer should have a positive slope and a y-intercept of { 2.00 $}$ dollars.

Based on the graph, the answer that matches the given equation is:

  • The cost of the taxi ride increases as the number of minutes increases.
  • The y-intercept represents the initial cost of the taxi ride, which is { 2.00 $}$ dollars.
  • The slope of the graph is { 3 $}$, which represents the increase in cost per minute.

In conclusion, the cost function of a taxi ride is a simple linear equation that can be graphed on a coordinate plane. By analyzing the graph, we can determine which answer matches the given equation. The answer should have a positive slope and a y-intercept of { 2.00 $}$ dollars.
The Cost of a Taxi Ride: Q&A

In our previous article, we explored the cost function of a taxi ride, which is given by the equation { c(x) = 3x + 2.00 $}$, where { x $}$ represents the number of minutes. We graphed this function on a piece of paper and analyzed the results to determine which answer matches the given equation. In this article, we will answer some frequently asked questions about the cost of a taxi ride.

Q: What is the cost of a taxi ride for 10 minutes?

A: To find the cost of a taxi ride for 10 minutes, we need to plug in { x = 10 $}$ into the equation { c(x) = 3x + 2.00 $}$.

{ c(10) = 3(10) + 2.00 $}$

Simplifying the equation gives us:

{ c(10) = 30 + 2.00 $}$

{ c(10) = 32.00 $}$

So, the cost of a taxi ride for 10 minutes is { 32.00 $}$.

Q: What is the cost of a taxi ride for 5 minutes?

A: To find the cost of a taxi ride for 5 minutes, we need to plug in { x = 5 $}$ into the equation { c(x) = 3x + 2.00 $}$.

{ c(5) = 3(5) + 2.00 $}$

Simplifying the equation gives us:

{ c(5) = 15 + 2.00 $}$

{ c(5) = 17.00 $}$

So, the cost of a taxi ride for 5 minutes is { 17.00 $}$.

Q: What is the initial cost of a taxi ride?

A: The initial cost of a taxi ride is represented by the y-intercept of the graph, which is { 2.00 $}$.

Q: What is the increase in cost per minute?

A: The increase in cost per minute is represented by the slope of the graph, which is { 3 $}$.

Q: How can I use the cost function to estimate the cost of a taxi ride?

A: To estimate the cost of a taxi ride, you can plug in the number of minutes into the equation { c(x) = 3x + 2.00 $}$. This will give you an estimate of the cost of the taxi ride.

Q: What are some real-world applications of the cost function?

A: The cost function has many real-world applications, such as:

  • Estimating the cost of a taxi ride
  • Calculating the cost of a trip
  • Determining the cost of a service
  • Analyzing the cost of a product

In conclusion, the cost function of a taxi ride is a simple linear equation that can be used to estimate the cost of a taxi ride. By plugging in the number of minutes into the equation { c(x) = 3x + 2.00 $}$, we can estimate the cost of the taxi ride. The cost function has many real-world applications, such as estimating the cost of a trip, calculating the cost of a service, and determining the cost of a product.

In conclusion, the cost function of a taxi ride is a useful tool for estimating the cost of a taxi ride. By understanding the cost function, we can make informed decisions about our transportation costs.