Given below are descriptions of two lines. Line 1: Goes through \( (12,-16) \) and \( (11,-14) \) Line 2: Goes through \( (4,-29) \) and \( (9,-74) \) The slope of Line 1 is \( m= \) The slope of Line 2 is \( m= \) Finally, which of the following is true? Line 1 is parallel to Line 2. Line 1 is perpendicular to Line 2 Line 1 is neither parallel nor perpendicular to Line 2 Question Help: Submit Question 1 Video 1 Video 2 Video 3

To find the slopes of the two lines, we can use the formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] ### Step 1: Calculate the slope of Line 1 For Line 1, the points are \( (12, -16) \) and \( (11, -14) \). Using the slope formula: \[ m_1 = \frac{-14 - (-16)}{11 - 12} \] Calculating the numerator and denominator: \[ m_1 = \frac{-14 + 16}{11 - 12} = \frac{2}{-1} = -2 \] ### Step 2: Calculate the slope of Line 2 For Line 2, the points are \( (4, -29) \) and \( (9, -74) \). Using the slope formula: \[ m_2 = \frac{-74 - (-29)}{9 - 4} \] Calculating the numerator and denominator: \[ m_2 = \frac{-74 + 29}{9 - 4} = \frac{-45}{5} = -9 \] ### Step 3: Determine the relationship between the lines Now we have the slopes: - Slope of Line 1: \( m_1 = -2 \) - Slope of Line 2: \( m_2 = -9 \) To determine if the lines are parallel, perpendicular, or neither: - Lines are parallel if their slopes are equal: \( m_1 = m_2 \) - Lines are perpendicular if the product of their slopes is \(-1\): \( m_1 \cdot m_2 = -1 \) Calculating the product of the slopes: \[ m_1 \cdot m_2 = (-2) \cdot (-9) = 18 \] Since \( 18 \neq -1 \) and \( -2 \neq -9 \), we conclude that: - Line 1 is neither parallel nor perpendicular to Line 2. ### Final Results - The slope of Line 1 is \( m_1 = -2 \). - The slope of Line 2 is \( m_2 = -9 \). - Therefore, the correct statement is: **Line 1 is neither parallel nor perpendicular to Line 2.**