Question

If the line through \( (3, y) \) and \( (2, 7) \) is parallel to the line through \( (-1, 4) \) and \( (0, 6) \), then the value of \( y \) is:

• A. -7
• B. 9
• C. 7
• D. 2

Hint:

For parallel lines, set the slopes equal to each other and solve for the unknown variable.

Answer 1

The Correct Option is B

Step 1: Find the slope of the line through \( (-1, 4) \) and \( (0, 6) \).
The slope \( m \) of a line through points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For the points \( (-1, 4) \) and \( (0, 6) \), the slope is: \[ m = \frac{6 - 4}{0 - (-1)} = \frac{2}{1} = 2 \]

Step 2: Use the slope condition for parallel lines.
Since the line through \( (3, y) \) and \( (2, 7) \) is parallel to the line through \( (-1, 4) \) and \( (0, 6) \), they must have the same slope. Thus, the slope of the line through \( (3, y) \) and \( (2, 7) \) must also be 2. The slope of the line through \( (3, y) \) and \( (2, 7) \) is: \[ m = \frac{7 - y}{2 - 3} = \frac{7 - y}{-1} = y - 7 \] Setting this equal to 2: \[ y - 7 = 2 \] \[ y = 9 \] Thus, the value of \( y \) is 9. Therefore, the correct answer is 2. 9.