Question
x - time (minutes) 8 5 7 2 9 y - distance (meters) 40 25 35 10 45 (4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a. Every minute meters are traveled. b. Write an equation to show the relationship between x and y. c. The relationship is because the y-intercept is Question 3 4. Use the graph to match the responses. (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The y-intercept An equation that represents this graph. The constant of proportionality Question 4 5. The equation of this graph is y = 23x − 4 What transformation would need to happen for the equation of the line to be y = 23x ? (1 point) Responses Shift the graph up 4 Shift the graph up 4 Shift the graph left 4 Shift the graph left 4 Shift the graph down 3 and left 2 Shift the graph down 3 and left 2 Shift the graph right 3, down 2 Shift the graph right 3, down 2 Question 5 6. A cab company charges $8 per mile for a lift to the airport. What change would the company make to their charges to make this a non proportional situation? (1 point) Responses Charge $12 per mile instead of $8 Charge $12 per mile instead of $8 Charge a flat rate of $10 and then $8 per mile Charge a flat rate of $10 and then $8 per mile No changes are needed No changes are needed Charge $4 per mile instead of $8 Charge $4 per mile instead of $8 Question 6 7. One business charges $12 per t-shirt custom made. Another business charges $11 per t-shirt plus a $20 set up fee for custom made. If you were to graph both of these scenarios on the coordinate plane, the first graph would be proportional and the second non proportional. How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph? (1 point) Responses Right 20 Right 20 Left 1 Left 1 Left 20 Left 20 Right 1 Right 1 Up 1 Up 1 Up 20 Up 20 Skip to navigation
Answers
GPT-4o mini
Let's break down each question step-by-step and fill in the correct responses based on the provided information.
**Question 1: (4 points)**
**x - time (minutes):** 8, 5, 7, 2, 9
**y - distance (meters):** 40, 25, 35, 10, 45
a. **Every minute meters are traveled.**
Let's find the constant of proportionality by calculating the ratio of distance to time for each pair:
- For 8 minutes: \( \frac{40}{8} = 5\)
- For 5 minutes: \( \frac{25}{5} = 5\)
- For 7 minutes: \( \frac{35}{7} = 5\)
- For 2 minutes: \( \frac{10}{2} = 5\)
- For 9 minutes: \( \frac{45}{9} = 5\)
So the correct answer is **5** meters per minute.
b. **Write an equation to show the relationship between x and y.**
The relationship is linear, and it can be expressed as \( y = mx + b \) where \( m \) is the slope (5), and since at zero time, the distance is presumably zero (based on the previous calculations), the equation is \( y = 5x\).
So the equation is: **y = 5x**.
c. **The relationship is because the y-intercept is 0.**
Since the graph passes through the origin, the y-intercept is indeed 0.
---
**Question 4: (3 points)**
1. **The y-intercept.**
Since the line's equation provided is \( y = 23x - 4 \), the y-intercept is **-4**.
2. **An equation that represents this graph.**
This matches with the previous part: **y = 23x - 4** (the provided information).
3. **The constant of proportionality.**
The constant of proportionality is the coefficient of x, which in this case is **23**.
---
**Question 5: (1 point)**
The equation that needs to change is \( y = 23x - 4 \) to become \( y = 23x \).
To do this, you would **Shift the graph up 4**.
---
**Question 6: (1 point)**
For the cab company, changing the pricing to **Charge a flat rate of $10 and then $8 per mile** would make it a non-proportional situation, because a flat rate adds a constant cost regardless of the distance traveled.
---
**Question 7: (1 point)**
To transform the first graph (which is proportional) to have the same y-intercept as the second graph (which has a setup fee of $20), you would **Left 20** to decrease the initial cost to match the $20 setup fee.
---
Feel free to clarify or ask for more specific assistance on any of these questions!
**Question 1: (4 points)**
**x - time (minutes):** 8, 5, 7, 2, 9
**y - distance (meters):** 40, 25, 35, 10, 45
a. **Every minute meters are traveled.**
Let's find the constant of proportionality by calculating the ratio of distance to time for each pair:
- For 8 minutes: \( \frac{40}{8} = 5\)
- For 5 minutes: \( \frac{25}{5} = 5\)
- For 7 minutes: \( \frac{35}{7} = 5\)
- For 2 minutes: \( \frac{10}{2} = 5\)
- For 9 minutes: \( \frac{45}{9} = 5\)
So the correct answer is **5** meters per minute.
b. **Write an equation to show the relationship between x and y.**
The relationship is linear, and it can be expressed as \( y = mx + b \) where \( m \) is the slope (5), and since at zero time, the distance is presumably zero (based on the previous calculations), the equation is \( y = 5x\).
So the equation is: **y = 5x**.
c. **The relationship is because the y-intercept is 0.**
Since the graph passes through the origin, the y-intercept is indeed 0.
---
**Question 4: (3 points)**
1. **The y-intercept.**
Since the line's equation provided is \( y = 23x - 4 \), the y-intercept is **-4**.
2. **An equation that represents this graph.**
This matches with the previous part: **y = 23x - 4** (the provided information).
3. **The constant of proportionality.**
The constant of proportionality is the coefficient of x, which in this case is **23**.
---
**Question 5: (1 point)**
The equation that needs to change is \( y = 23x - 4 \) to become \( y = 23x \).
To do this, you would **Shift the graph up 4**.
---
**Question 6: (1 point)**
For the cab company, changing the pricing to **Charge a flat rate of $10 and then $8 per mile** would make it a non-proportional situation, because a flat rate adds a constant cost regardless of the distance traveled.
---
**Question 7: (1 point)**
To transform the first graph (which is proportional) to have the same y-intercept as the second graph (which has a setup fee of $20), you would **Left 20** to decrease the initial cost to match the $20 setup fee.
---
Feel free to clarify or ask for more specific assistance on any of these questions!