Question
Which graph represents the equation y equals one half times x plus 2?
Group of answer choices
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Flag question: Question 2
Question 20.33 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $80, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised (y) and the number of students who attend the dance (x)?
Group of answer choices
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 60
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 80 through the point 2 comma 60
Flag question: Question 3
Question 30.34 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7
Find and interpret the slope and y-intercept in this real-world situation.
Group of answer choices
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
Group of answer choices
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Flag question: Question 2
Question 20.33 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $80, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised (y) and the number of students who attend the dance (x)?
Group of answer choices
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 60
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 80 through the point 2 comma 60
Flag question: Question 3
Question 30.34 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7
Find and interpret the slope and y-intercept in this real-world situation.
Group of answer choices
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
Answers
Answered by
GPT-4o mini
Let's analyze each question and find the correct answers.
### Question 1
**Identify the correct graph for the equation:**
\( y = \frac{1}{2}x + 2 \)
This equation is in slope-intercept form \( y = mx + b \), where:
- \( m = \frac{1}{2} \) (slope)
- \( b = 2 \) (y-intercept)
The y-intercept indicates that the graph crosses the y-axis at \( (0, 2) \). To find another point, we can use the slope:
- For every 2 units increase in x, y increases by 1 unit (since the slope is \( \frac{1}{2} \)).
Using the y-intercept \( (0, 2) \), if \( x = -4 \):
- \( y = \frac{1}{2}(-4) + 2 = -2 + 2 = 0 \)
So the graph goes through the point \( (-4, 0) \).
The only option given that fits this line is:
- **graph of a line passing through the points (-4, 0) and (0, 2)**.
### Question 2
**Identify the graph that describes the revenue from a dance:**
Decorations cost $80, and the club charges $10 per student.
The relationship can be established as follows:
- **Cost (fixed):** $80 (the club needs to cover this before making a profit)
- **Revenue:** $10 for each student attended (linear relation).
The revenue can be expressed as:
- \( y = 10x - 80 \)
This equation means that when there are 0 students, the amount of money raised is -80 (covering costs).
- If \( x = 2 \):
\( y = 10(2) - 80 = 20 - 80 = -60 \).
Now we need to find the graph passing through:
- \( (0, -80) \) and \( (2, -60) \).
Thus the option that fits this scenario is:
- **graph with the x-axis labeled number of students and the y-axis labeled amount of money raised and a line going from the point (0, -80) through the point (2, -60)**.
### Question 3
**Analyzing the height of the candlesticks over time:**
- **Graph:** starting at the point (0, 9) and going to the point (3, 7).
The slope is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 9}{3 - 0} = \frac{-2}{3}
\]
This implies that for every hour that passes, the height decreases by \(\frac{2}{3}\) inch.
The y-intercept is 9, indicating that at time \( t = 0 \) (the start), the height of the candlestick is 9 inches.
Thus the correct interpretation is:
- **The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.**
In summary:
- **Question 1:** graph through (-4, 0) and (0, 2)
- **Question 2:** graph through (0, -80) and (2, -60)
- **Question 3:** The slope is negative two thirds, and the y-intercept is 9.
### Question 1
**Identify the correct graph for the equation:**
\( y = \frac{1}{2}x + 2 \)
This equation is in slope-intercept form \( y = mx + b \), where:
- \( m = \frac{1}{2} \) (slope)
- \( b = 2 \) (y-intercept)
The y-intercept indicates that the graph crosses the y-axis at \( (0, 2) \). To find another point, we can use the slope:
- For every 2 units increase in x, y increases by 1 unit (since the slope is \( \frac{1}{2} \)).
Using the y-intercept \( (0, 2) \), if \( x = -4 \):
- \( y = \frac{1}{2}(-4) + 2 = -2 + 2 = 0 \)
So the graph goes through the point \( (-4, 0) \).
The only option given that fits this line is:
- **graph of a line passing through the points (-4, 0) and (0, 2)**.
### Question 2
**Identify the graph that describes the revenue from a dance:**
Decorations cost $80, and the club charges $10 per student.
The relationship can be established as follows:
- **Cost (fixed):** $80 (the club needs to cover this before making a profit)
- **Revenue:** $10 for each student attended (linear relation).
The revenue can be expressed as:
- \( y = 10x - 80 \)
This equation means that when there are 0 students, the amount of money raised is -80 (covering costs).
- If \( x = 2 \):
\( y = 10(2) - 80 = 20 - 80 = -60 \).
Now we need to find the graph passing through:
- \( (0, -80) \) and \( (2, -60) \).
Thus the option that fits this scenario is:
- **graph with the x-axis labeled number of students and the y-axis labeled amount of money raised and a line going from the point (0, -80) through the point (2, -60)**.
### Question 3
**Analyzing the height of the candlesticks over time:**
- **Graph:** starting at the point (0, 9) and going to the point (3, 7).
The slope is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 9}{3 - 0} = \frac{-2}{3}
\]
This implies that for every hour that passes, the height decreases by \(\frac{2}{3}\) inch.
The y-intercept is 9, indicating that at time \( t = 0 \) (the start), the height of the candlestick is 9 inches.
Thus the correct interpretation is:
- **The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.**
In summary:
- **Question 1:** graph through (-4, 0) and (0, 2)
- **Question 2:** graph through (0, -80) and (2, -60)
- **Question 3:** The slope is negative two thirds, and the y-intercept is 9.