Question
2. Given the table for x, lawns mowed and y, money earned: x - # of lawns 7 6 2 9 3 y - $ earned 294 252 84 378 126 (4 points) a. Every lawn mowed is -blank- dollars earned. b. Dollars/1 lawn mowed is called a -blank- c. This relationship is -blank- because -blank- tickets sold is $0 earned.
Answers
Answer
for b you meant unit rate yes?
Answer
any other terms other than linear I can put there
Answer
you meant proportional yes?
Answer
3. Given the table for x, time in minutes and y, distance traveled in meters: x - time (minutes) 8 5 7 2 9 y - distance (meters) 40 25 35 10 45 (4 points) a. Every minute Response area meters are traveled. b. Write an equation to show the relationship between x and y. Response area c. The relationship is Response area because the y-intercept is Response area
Answer
for linear you also mean proportional and (0,0) correct?
Answered by
GPT-4o mini
To answer the questions based on the given data set:
Given the table:
- For \( x \) (lawns mowed) and \( y \) (money earned):
- \( x = 7 \), \( y = 294 \)
- \( x = 6 \), \( y = 252 \)
- \( x = 2 \), \( y = 84 \)
- \( x = 9 \), \( y = 378 \)
- \( x = 3 \), \( y = 126 \)
### a. Every lawn mowed is **$42** dollars earned.
To find out how much money is earned per lawn mowed, you can divide the total money earned by the number of lawns mowed.
For example:
- For \( x = 7 \), \( y = 294 \):
\[
\frac{294}{7} = 42
\]
- This calculation holds true for the other pairs as well.
### b. Dollars/1 lawn mowed is called a **rate**.
In this context, the rate represents the amount earned per each lawn mowed (i.e., the earning per lawn).
### c. This relationship is **linear** because **0 tickets sold is $0 earned**.
In a linear relationship, if one variable is zero, the other is also zero. Here, if no lawns are mowed (0 lawns), then the money earned (y) is also $0, reflecting a direct proportionality between the number of lawns mowed and the money earned.
So, filling in the blanks:
a. **$42**
b. **rate**
c. **linear** because **0 tickets sold is $0 earned**.
Given the table:
- For \( x \) (lawns mowed) and \( y \) (money earned):
- \( x = 7 \), \( y = 294 \)
- \( x = 6 \), \( y = 252 \)
- \( x = 2 \), \( y = 84 \)
- \( x = 9 \), \( y = 378 \)
- \( x = 3 \), \( y = 126 \)
### a. Every lawn mowed is **$42** dollars earned.
To find out how much money is earned per lawn mowed, you can divide the total money earned by the number of lawns mowed.
For example:
- For \( x = 7 \), \( y = 294 \):
\[
\frac{294}{7} = 42
\]
- This calculation holds true for the other pairs as well.
### b. Dollars/1 lawn mowed is called a **rate**.
In this context, the rate represents the amount earned per each lawn mowed (i.e., the earning per lawn).
### c. This relationship is **linear** because **0 tickets sold is $0 earned**.
In a linear relationship, if one variable is zero, the other is also zero. Here, if no lawns are mowed (0 lawns), then the money earned (y) is also $0, reflecting a direct proportionality between the number of lawns mowed and the money earned.
So, filling in the blanks:
a. **$42**
b. **rate**
c. **linear** because **0 tickets sold is $0 earned**.
Answered by
GPT-4o mini
Yes, you're correct! In the context of the problem, the term **"unit rate"** is indeed more precise than just "rate." The unit rate specifically refers to the amount earned per one lawn mowed, which is $42 in this case.
So, to clarify:
### b. Dollars/1 lawn mowed is called a **unit rate**.
Thank you for pointing that out!
So, to clarify:
### b. Dollars/1 lawn mowed is called a **unit rate**.
Thank you for pointing that out!
Answered by
GPT-4o mini
Certainly! In addition to "linear," you can use several other terms to describe the relationship between the number of lawns mowed and the money earned based on the provided data. Here are a few alternatives:
1. **Directly Proportional**: This term highlights that as the number of lawns mowed increases, the amount of money earned increases at a constant rate.
2. **Constant Rate of Change**: This emphasizes that the change in money earned is consistent for each additional lawn mowed.
3. **Proportional Relationship**: Similar to directly proportional, it signifies that the earnings are directly related to the number of lawns mowed.
4. **Linear Function**: This elaborates on the linearity concept while indicating it describes a function where the output is directly related to the input.
So, you could modify part c of your answer as follows:
### c. This relationship is **directly proportional** because **0 lawns mowed is $0 earned**.
Feel free to choose the term that best fits your understanding of the relationship!
1. **Directly Proportional**: This term highlights that as the number of lawns mowed increases, the amount of money earned increases at a constant rate.
2. **Constant Rate of Change**: This emphasizes that the change in money earned is consistent for each additional lawn mowed.
3. **Proportional Relationship**: Similar to directly proportional, it signifies that the earnings are directly related to the number of lawns mowed.
4. **Linear Function**: This elaborates on the linearity concept while indicating it describes a function where the output is directly related to the input.
So, you could modify part c of your answer as follows:
### c. This relationship is **directly proportional** because **0 lawns mowed is $0 earned**.
Feel free to choose the term that best fits your understanding of the relationship!
Answered by
GPT-4o mini
Yes, you're right. The term **"proportional"** is indeed the more concise way to describe the relationship between the number of lawns mowed and the money earned. Here’s the revised phrasing:
### c. This relationship is **proportional** because **0 lawns mowed is $0 earned**.
Thank you for your attention to detail! "Proportional" captures the essential characteristic of the relationship without being overly complex.
### c. This relationship is **proportional** because **0 lawns mowed is $0 earned**.
Thank you for your attention to detail! "Proportional" captures the essential characteristic of the relationship without being overly complex.
Answered by
GPT-4o mini
To analyze the given data for time in minutes (x) and distance traveled in meters (y), let's break down the questions step by step.
### Given:
- **x (time in minutes)**: 8, 5, 7, 2, 9
- **y (distance in meters)**: 40, 25, 35, 10, 45
### a. Every minute **5** meters are traveled.
To find the distance traveled per minute, you can divide the distance by the time for each pair:
- For \( x = 8, y = 40 \): \( \frac{40}{8} = 5 \)
- For \( x = 5, y = 25 \): \( \frac{25}{5} = 5 \)
- For \( x = 7, y = 35 \): \( \frac{35}{7} = 5 \)
- For \( x = 2, y = 10 \): \( \frac{10}{2} = 5 \)
- For \( x = 9, y = 45 \): \( \frac{45}{9} = 5 \)
This shows that every minute, **5 meters** are consistently traveled.
### b. Write an equation to show the relationship between x and y.
From our earlier calculations, we can see that the distance traveled is directly proportional to the time spent. The relationship can be expressed as:
\[
y = 5x
\]
where \( y \) is the distance (in meters) and \( x \) is the time (in minutes).
### c. The relationship is **linear** because the y-intercept is **0**.
Since the equation \( y = 5x \) indicates a straight-line relationship through the origin (0,0), we can conclude that:
- The relationship is linear because it follows the form of a linear equation, and
- The y-intercept is 0, which means that if no time is taken (0 minutes), the distance traveled is also 0 meters.
### Summary of Answers:
a. Every minute **5** meters are traveled.
b. Write an equation to show the relationship between x and y: **y = 5x**
c. The relationship is **linear** because the y-intercept is **0**.
### Given:
- **x (time in minutes)**: 8, 5, 7, 2, 9
- **y (distance in meters)**: 40, 25, 35, 10, 45
### a. Every minute **5** meters are traveled.
To find the distance traveled per minute, you can divide the distance by the time for each pair:
- For \( x = 8, y = 40 \): \( \frac{40}{8} = 5 \)
- For \( x = 5, y = 25 \): \( \frac{25}{5} = 5 \)
- For \( x = 7, y = 35 \): \( \frac{35}{7} = 5 \)
- For \( x = 2, y = 10 \): \( \frac{10}{2} = 5 \)
- For \( x = 9, y = 45 \): \( \frac{45}{9} = 5 \)
This shows that every minute, **5 meters** are consistently traveled.
### b. Write an equation to show the relationship between x and y.
From our earlier calculations, we can see that the distance traveled is directly proportional to the time spent. The relationship can be expressed as:
\[
y = 5x
\]
where \( y \) is the distance (in meters) and \( x \) is the time (in minutes).
### c. The relationship is **linear** because the y-intercept is **0**.
Since the equation \( y = 5x \) indicates a straight-line relationship through the origin (0,0), we can conclude that:
- The relationship is linear because it follows the form of a linear equation, and
- The y-intercept is 0, which means that if no time is taken (0 minutes), the distance traveled is also 0 meters.
### Summary of Answers:
a. Every minute **5** meters are traveled.
b. Write an equation to show the relationship between x and y: **y = 5x**
c. The relationship is **linear** because the y-intercept is **0**.
Answered by
GPT-4o mini
Yes, that's correct! Both **linear** and **proportional** can be used in this context, especially since the relationship represented by the equation \( y = 5x \) is a direct proportionality. The point \( (0,0) \) indicates that when the time (x) is zero, the distance (y) is also zero, reinforcing the idea that this relationship is proportional as well.
Here's the refined answer for part c:
### c. The relationship is **proportional** (or **linear**) because the y-intercept is **(0,0)**.
Both terms accurately reflect the nature of the relationship, and \( (0,0) \) specifically stands for the point where both variables are zero, further demonstrating that they are directly related. You can use either term based on your preference. Thank you for your clarification!
Here's the refined answer for part c:
### c. The relationship is **proportional** (or **linear**) because the y-intercept is **(0,0)**.
Both terms accurately reflect the nature of the relationship, and \( (0,0) \) specifically stands for the point where both variables are zero, further demonstrating that they are directly related. You can use either term based on your preference. Thank you for your clarification!