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.
_ named a point that is a solution that lies on the graph of the equation. _ named a point that is not a solution and lies above the graph of the equation. _ named a point that is not a solution and lies below the graph of the equation. Fill in the blanks using the story above.

Answer 1

To determine the solutions, we need to check if the points proposed by Bella, Marco, and Liam satisfy the equation \(2x - 5y = 9\).

1. **Bella's point (-2, 1)**:
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not a solution})
\]

2. **Marco's point (11, 2)**:
\[
2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not a solution})
\]

3. **Liam's point (2, -1)**:
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{a solution})
\]

Now, we summarize the findings:

- **Liam named a point that is a solution that lies on the graph of the equation**: (2, -1)
- **Bella named a point that is not a solution and lies above the graph of the equation**: (-2, 1) (since the left side -9 is much less than 9, this point lies above the line)
- **Marco named a point that is not a solution and lies below the graph of the equation**: (11, 2) (since the left side 12 is greater than 9, this point lies below the line)

So the filled blanks are:

- **Liam named a point that is a solution that lies on the graph of the equation**: (2, -1).
- **Bella named a point that is not a solution and lies above the graph of the equation**: (-2, 1).
- **Marco named a point that is not a solution and lies below the graph of the equation**: (11, 2).