If the xy-plane, which of the following ordered pairs is a point on the line `y=2x-6`?

Options

A. `(6, 7)`
B. `(7, 7)`
C. `(7, 8)`
D. `(8, 7)`

Answer

To determine which of the given ordered pairs is a point on the line defined by the equation \( y = 2x - 6 \), we will check each ordered pair by substituting the x-value into the equation and verifying if the resulting y-value matches the y-value of the ordered pair.

### Step-by-Step Solution:

1. **Identify the Ordered Pairs**: We need to check the following ordered pairs:
- A: (6, 7)
- B: (7, 7)
- C: (7, 8)
- D: (8, 7)

2. **Check Ordered Pair A: (6, 7)**:
- Substitute \( x = 6 \) into the equation:
\[ y = 2(6) - 6 = 12 - 6 = 6 \]
- Compare with the y-value in the ordered pair:
\[ 7 \neq 6 \quad \text{(Incorrect)} \]

3. **Check Ordered Pair B: (7, 7)**:
- Substitute \( x = 7 \) into the equation:
\[ y = 2(7) - 6 = 14 - 6 = 8 \]
- Compare with the y-value in the ordered pair:
\[ 7 \neq 8 \quad \text{(Incorrect)} \]

4. **Check Ordered Pair C: (7, 8)**:
- Substitute \( x = 7 \) into the equation:
\[ y = 2(7) - 6 = 14 - 6 = 8 \]
- Compare with the y-value in the ordered pair:
\[ 8 = 8 \quad \text{(Correct)} \]

5. **Check Ordered Pair D: (8, 7)**:
- Substitute \( x = 8 \) into the equation:
\[ y = 2(8) - 6 = 16 - 6 = 10 \]
- Compare with the y-value in the ordered pair:
\[ 7 \neq 10 \quad \text{(Incorrect)} \]

### Conclusion:
The only ordered pair that lies on the line \( y = 2x - 6 \) is **C: (7, 8)**.