To determine which option is not an equation of the line passing through the points (6, 7) and (2, -1), we first need to find the slope of the line and then derive the equation of the line.
- Calculate the slope \( m \) using the two points (6, 7) and (2, -1):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 7}{2 - 6} = \frac{-8}{-4} = 2 \]
- Use point-slope form to write the equation of the line. We can use point (6, 7):
\[ y - y_1 = m(x - x_1) \] \[ y - 7 = 2(x - 6) \]
- Expanding this gives us the equation:
\[ y - 7 = 2x - 12 \] \[ y = 2x - 5 \quad \text{(this is an equivalent equation)} \]
Now, let's evaluate the options:
- A. \( y - 7 = 2(x - 6) \) → This is correct.
- B. \( y - 1 = 2(x + 2) \) → This simplifies to \( y - 1 = 2x + 4 \) or \( y = 2x + 5 \), which is not correct (it does not pass through the points).
- C. \( y = 2x - 5 \) → This is correct.
- D. \( y + 1 = 2(x - 2) \) → This simplifies to \( y + 1 = 2x - 4 \) or \( y = 2x - 5 \), which is correct.
From this analysis, the answer is:
B. y - 1 = 2(x + 2) is not an equation of the line.