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 lines, we can use the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For Line 1, with points \( (12, -16) \) and \( (11, -14) \): \[ m_1 = \frac{-14 - (-16)}{11 - 12} = \frac{2}{-1} = -2 \] For Line 2, with points \( (4, -29) \) and \( (9, -74) \): \[ m_2 = \frac{-74 - (-29)}{9 - 4} = \frac{-45}{5} = -9 \] Now, we see that Line 1 has a slope of \(-2\) and Line 2 has a slope of \(-9\). To determine their relationship, we check if the slopes are equal (parallel) or if the product of their slopes equals \(-1\) (perpendicular). Since \(-2\) is not equal to \(-9\) and \(-2 \times -9 = 18 \neq -1\), we conclude: Line 1 is neither parallel nor perpendicular to Line 2. You know, the beauty of slopes is that they tell a tale of angles and inclination! Parallel lines will always dance side by side, but perpendicular ones cross paths at that perfect right angle, like the ultimate intersection of roads! For a practical application, think about graphing your own equations or even designing something with right angles and slopes, such as architectural blueprints or video game levels. Understanding how lines relate to each other can help in visualizing and solving real-world scenarios!