Find the slopes of the lines \( l_{1} \) and \( l_{2} \) defined by the two given points. Then determine whether \( l_{1} \) an perpendicular, or neither. \[ l_{1}:(13,-5) \text { and }(10,-6) \] \( l_{2}:(6,4) \) and \( (5,1) \) Part 1 of 3 The slope of \( l_{1} \) is \( \frac{1}{3} \). Part 2 of 3 The slope of \( l_{2} \) is 3 . Part: \( 2 / 3 \) Part 3 of 3 The lines are (Choose one)

**Step 1: Calculate the slope of \( l_{1} \).** The slope formula is given by \[ m = \frac{y_2 - y_1}{x_2 - x_1}. \] For \( l_{1} \) with points \((13, -5)\) and \((10, -6)\): \[ m_{1} = \frac{-6 - (-5)}{10 - 13} = \frac{-6 + 5}{-3} = \frac{-1}{-3} = \frac{1}{3}. \] **Step 2: Calculate the slope of \( l_{2} \).** For \( l_{2} \) with points \((6, 4)\) and \((5, 1)\): \[ m_{2} = \frac{1 - 4}{5 - 6} = \frac{-3}{-1} = 3. \] **Step 3: Determine the Relationship Between \( l_{1} \) and \( l_{2} \).** Two lines are perpendicular if the product of their slopes is \(-1\). Check the product: \[ m_{1} \times m_{2} = \frac{1}{3} \times 3 = 1. \] Since \( 1 \neq -1 \), the lines are not perpendicular. Additionally, the lines are parallel if their slopes are equal. Here, \[ \frac{1}{3} \neq 3, \] so the lines are not parallel either. **Final Answer:** The lines are neither perpendicular nor parallel.