Let's start by solving the equation \(2x - 5 = 9\) for \(x\):
-
Add 5 to both sides: \[ 2x - 5 + 5 = 9 + 5 \] \[ 2x = 14 \]
-
Divide both sides by 2: \[ x = 7 \]
The solution to the equation is \(x = 7\). Now we will check each of the points provided to see if they are solutions.
-
Bella believes (-2, 1) is a solution:
- Substitute \(x = -2\) into the equation \(y = 2x - 5\): \[ y = 2(-2) - 5 = -4 - 5 = -9 \]
- Since \(y\) does not equal 1, this point is not a solution.
-
Marco believes (11, 2) is a solution:
- Substitute \(x = 11\): \[ y = 2(11) - 5 = 22 - 5 = 17 \]
- Since \(y\) does not equal 2, this point is not a solution.
-
Liam believes (2, -1) is a solution:
- Substitute \(x = 2\): \[ y = 2(2) - 5 = 4 - 5 = -1 \]
- Since \(y\) equals -1, this point is a solution.
Summary of findings:
- Liam's point (2, -1) is a solution to the equation.
- Bella's point (-2, 1) is not a solution and is below the graph of the equation since \(y = -9 < 1\).
- Marco's point (11, 2) is also not a solution and is above the graph of the equation since \(y = 17 > 2\).
Answering the blanks:
- A point that is a solution: (2, -1) (from Liam)
- A point that is not a solution and lies above the graph: (11, 2) (from Marco)
- A point that is not a solution and lies below the graph: (-2, 1) (from Bella)
1 answer