Let's first solve the equation \( 2x - 5 = 9 \) to find the actual solution.
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Add 5 to both sides: \[ 2x = 14 \]
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Divide by 2: \[ x = 7 \]
The point that corresponds to this solution is \( (7, y) \) for any value of \( y \). Since the equation is in terms of \( x \) only, we can say that any point on the line defined by this equation will have the x-coordinate of 7.
Now, let's evaluate the points proposed by the students:
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Bella's point: (-2,1) \[ 2(-2) - 5 = -4 - 5 = -9 \quad \text{(not a solution)} \]
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Marco's point: (11,2) \[ 2(11) - 5 = 22 - 5 = 17 \quad \text{(not a solution)} \]
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Liam's point: (2,-1) \[ 2(2) - 5 = 4 - 5 = -1 \quad \text{(not a solution)} \]
That means none of the students have suggested valid solutions.
Now, let's find points as requested:
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A point that is a solution:
- One solution is \( (7, 0) \). This means when \( x=7 \), we could choose \( y \) to be 0 (any \( y \) works).
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A point that is not a solution and lies above the graph:
- A point above the graph would have a y-value that is greater than what the equation provides for that x-value. For instance, you can take \( (7, 5) \): \[ 2(7) - 5 = 14 - 5 = 9 \quad \text{(y-value at x=7)} \] So \( (7, 5) \) is above the graph since 5 is greater than 0.
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A point that is not a solution and lies below the graph:
- A point below the graph could be \( (7, -1) \): \[ 2(7) - 5 = 14 - 5 = 9 \quad \text{(y-value at x=7)} \] Here, \( (7, -1) \) is below the graph since -1 is less than 0.
To summarize:
- A point that is a solution: (7, 0)
- A point that is not a solution and lies above the graph: (7, 5)
- A point that is not a solution and lies below the graph: (7, -1)