At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Let's consider the problem step-by-step to understand the given linear relationship:
1. Understanding the Question:
We need to analyze the relationship between the number of miles traveled (x) and the total fee (y) and identify what the [tex]\( y \)[/tex]-intercept represents in this context.
2. Data Points:
The table provided gives the total fee for various distances:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Miles} & \text{Total Fee} \\ \hline 2 & \$ 15.00 \\ \hline 5 & \$ 19.50 \\ \hline 7 & \$ 22.50 \\ \hline 10 & \$ 27.00 \\ \hline 15 & \$ 34.50 \\ \hline \end{array} \][/tex]
3. Concept of Linear Equation in Cab Fare:
The relationship between the distance (x) and the total fee (y) can be described using a linear equation of the form:
[tex]\[ y = mx + c \][/tex]
where [tex]\( m \)[/tex] is the slope of the line and [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept.
4. Slope (m):
The slope represents the rate of change in the fee with respect to distance. We determine it by taking any two points and computing:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the given data points, the calculations show that the slope (rate of increase per mile) is [tex]\( 1.5 \)[/tex].
5. Y-Intercept (c):
The [tex]\( y \)[/tex]-intercept in a linear equation represents the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. This is the starting fee or the base fare before any miles are traveled. The calculations indicate that this value (the base fare) is [tex]\( 12.0 \)[/tex].
6. Interpreting the Results:
Based on the results:
- The slope [tex]\( 1.5 \)[/tex] means that for every additional mile the cab travels, the total fee increases by \[tex]$1.50. - The \( y \)-intercept \( 12.0 \) means that when the cab travels 0 miles, the total fee will be \$[/tex]12.00.
7. Final Answers:
- When the cab travels 0 miles, the total fee will be \[tex]$12.00. - For every additional mile the cab travels, the total fee increases by \$[/tex]1.50.
Therefore, the correct interpretation for the [tex]\( y \)[/tex]-intercept in this context is:
When the cab travels 0 miles, the total fee will be \$ 12.00.
1. Understanding the Question:
We need to analyze the relationship between the number of miles traveled (x) and the total fee (y) and identify what the [tex]\( y \)[/tex]-intercept represents in this context.
2. Data Points:
The table provided gives the total fee for various distances:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Miles} & \text{Total Fee} \\ \hline 2 & \$ 15.00 \\ \hline 5 & \$ 19.50 \\ \hline 7 & \$ 22.50 \\ \hline 10 & \$ 27.00 \\ \hline 15 & \$ 34.50 \\ \hline \end{array} \][/tex]
3. Concept of Linear Equation in Cab Fare:
The relationship between the distance (x) and the total fee (y) can be described using a linear equation of the form:
[tex]\[ y = mx + c \][/tex]
where [tex]\( m \)[/tex] is the slope of the line and [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept.
4. Slope (m):
The slope represents the rate of change in the fee with respect to distance. We determine it by taking any two points and computing:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the given data points, the calculations show that the slope (rate of increase per mile) is [tex]\( 1.5 \)[/tex].
5. Y-Intercept (c):
The [tex]\( y \)[/tex]-intercept in a linear equation represents the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. This is the starting fee or the base fare before any miles are traveled. The calculations indicate that this value (the base fare) is [tex]\( 12.0 \)[/tex].
6. Interpreting the Results:
Based on the results:
- The slope [tex]\( 1.5 \)[/tex] means that for every additional mile the cab travels, the total fee increases by \[tex]$1.50. - The \( y \)-intercept \( 12.0 \) means that when the cab travels 0 miles, the total fee will be \$[/tex]12.00.
7. Final Answers:
- When the cab travels 0 miles, the total fee will be \[tex]$12.00. - For every additional mile the cab travels, the total fee increases by \$[/tex]1.50.
Therefore, the correct interpretation for the [tex]\( y \)[/tex]-intercept in this context is:
When the cab travels 0 miles, the total fee will be \$ 12.00.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
