Question 2 of 10

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.

1. **Calculate the slope \( m \)** using the two points (6, 7) and (2, -1):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 7}{2 - 6} = \frac{-8}{-4} = 2
\]

2. **Use point-slope form to write the equation of the line**. We can use point (6, 7):

\[
y - y_1 = m(x - x_1)
\]
\[
y - 7 = 2(x - 6)
\]

3. 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.