One line passes through the points \( (-6,0) \) and \( (-4,6) \). Another line passes through points \( (5,-2) \) and \( (8,7) \). Are the lines parallel, perpendicular, or neither? Choose 1 answer: (A) Parallel (B) Perpendicular (C) Neither

To determine the relationship between the two lines, we need to find the slopes of each line. 1. **Calculate the slope of the first line** that passes through the points \( (-6,0) \) and \( (-4,6) \). The formula for the slope \( m \) between two 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 first line: - \( (x_1, y_1) = (-6, 0) \) - \( (x_2, y_2) = (-4, 6) \) Substituting these values into the slope formula: \[ m_1 = \frac{6 - 0}{-4 - (-6)} = \frac{6}{-4 + 6} = \frac{6}{2} = 3 \] 2. **Calculate the slope of the second line** that passes through the points \( (5,-2) \) and \( (8,7) \). For the second line: - \( (x_1, y_1) = (5, -2) \) - \( (x_2, y_2) = (8, 7) \) Substituting these values into the slope formula: \[ m_2 = \frac{7 - (-2)}{8 - 5} = \frac{7 + 2}{3} = \frac{9}{3} = 3 \] 3. **Compare the slopes**: - The slope of the first line \( m_1 = 3 \) - The slope of the second line \( m_2 = 3 \) Since both slopes are equal, the lines are **parallel**. Thus, the answer is: (A) Parallel