Question
Ms. Mac asked her students to determine a solution for 2x−5y=9
.
Bella believes (-2, 1) is a solution to the equation.
Marco believes (11, 2) is a solution to the equation.
Liam believes (2, -1)is a solution to the equation.
(1 point)
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.
Response area named a point that is a solution that lies on the graph of the equation. Response area named a point that is not a solution and lies above the graph of the equation. Response area named a point that is not a solution and lies below the graph of the equation.
.
Bella believes (-2, 1) is a solution to the equation.
Marco believes (11, 2) is a solution to the equation.
Liam believes (2, -1)is a solution to the equation.
(1 point)
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.
Response area named a point that is a solution that lies on the graph of the equation. Response area named a point that is not a solution and lies above the graph of the equation. Response area named a point that is not a solution and lies below the graph of the equation.
Answers
GPT-4o mini
To determine which of the given points are solutions to the equation \( 2x - 5y = 9 \), we can plug in the coordinates of each point into the equation and check if it holds true.
1. **For Bella's point (-2, 1):**
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not a solution})
\]
2. **For Marco's point (11, 2):**
\[
2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not a solution})
\]
3. **For Liam's point (2, -1):**
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{a solution})
\]
Now, we can categorize the points based on whether they are solutions and their relative position to the graph of the equation \( 2x - 5y = 9 \).
- **Point that is a solution:** (2, -1)
- **Point that is not a solution and lies above the graph:** Since (-2, 1) gave us -9 (less than 9), it lies above the graph.
- **Point that is not a solution and lies below the graph:** Marco's point (11, 2) gave us 12 (greater than 9), so it lies below the graph.
So the responses are:
1. **Point that is a solution:** (2, -1)
2. **Point that is not a solution and lies above the graph:** (-2, 1)
3. **Point that is not a solution and lies below the graph:** (11, 2)
1. **For Bella's point (-2, 1):**
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not a solution})
\]
2. **For Marco's point (11, 2):**
\[
2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not a solution})
\]
3. **For Liam's point (2, -1):**
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{a solution})
\]
Now, we can categorize the points based on whether they are solutions and their relative position to the graph of the equation \( 2x - 5y = 9 \).
- **Point that is a solution:** (2, -1)
- **Point that is not a solution and lies above the graph:** Since (-2, 1) gave us -9 (less than 9), it lies above the graph.
- **Point that is not a solution and lies below the graph:** Marco's point (11, 2) gave us 12 (greater than 9), so it lies below the graph.
So the responses are:
1. **Point that is a solution:** (2, -1)
2. **Point that is not a solution and lies above the graph:** (-2, 1)
3. **Point that is not a solution and lies below the graph:** (11, 2)
the answer choices are
marco
liam
bella
marco
liam
bella
GPT-4o mini
Thank you for providing the answer choices. Based on the previous analysis, here's how the points correspond to the answer choices:
- **Liam (2, -1)** is a solution to the equation \( 2x - 5y = 9 \).
- **Bella (-2, 1)** is not a solution and lies above the graph (since it yields -9, which is less than 9).
- **Marco (11, 2)** is not a solution and lies below the graph (since it yields 12, which is greater than 9).
Now, aligning to the given response areas:
1. **Point that is a solution that lies on the graph of the equation:** **liam**
2. **Point that is not a solution and lies above the graph of the equation:** **bella**
3. **Point that is not a solution and lies below the graph of the equation:** **marco**
So you would place the names as follows:
- **Liam** in the solution area.
- **Bella** in the area for not a solution and above the graph.
- **Marco** in the area for not a solution and below the graph.
- **Liam (2, -1)** is a solution to the equation \( 2x - 5y = 9 \).
- **Bella (-2, 1)** is not a solution and lies above the graph (since it yields -9, which is less than 9).
- **Marco (11, 2)** is not a solution and lies below the graph (since it yields 12, which is greater than 9).
Now, aligning to the given response areas:
1. **Point that is a solution that lies on the graph of the equation:** **liam**
2. **Point that is not a solution and lies above the graph of the equation:** **bella**
3. **Point that is not a solution and lies below the graph of the equation:** **marco**
So you would place the names as follows:
- **Liam** in the solution area.
- **Bella** in the area for not a solution and above the graph.
- **Marco** in the area for not a solution and below the graph.