29) through: \( (3,-1) \) and \( (-4,-1) \) 30) through: \( (5,5) \) and \( (-2,0) \) 1) through: \( (0,-5) \) and \( (-2,-5) \) 32) through: \( (-4,2) \) and \( (-2,1) \) 3) through: \( (0,4) \) and \( (-3,1) \) 34) through: \( (0,-4) \) and \( (-2,-1) \) 5) through: \( (-4,-4) \) and \( (0,-3) \) 36) through: \( (0,1) \) and \( (-2,5) \) 7) through: \( (-1,-1) \) and \( (-3,0) \) 38) through: \( (0,3) \) and \( (-4,2) \) 9) through: \( (-5,0) \) and \( (-5,-3) \) 40) through: \( (2,0) \) and \( (-4,5) \)

Sure! Below are the equations of the lines passing through each pair of points you've provided: --- **1)** Through: \( (0, -5) \) and \( (-2, -5) \) - **Type:** Horizontal Line - **Equation:** \[ y = -5 \] --- **3)** Through: \( (0, 4) \) and \( (-3, 1) \) - **Slope Calculation:** \[ m = \frac{1 - 4}{-3 - 0} = \frac{-3}{-3} = 1 \] - **Equation:** \[ y = x + 4 \] --- **5)** Through: \( (-4, -4) \) and \( (0, -3) \) - **Slope Calculation:** \[ m = \frac{-3 - (-4)}{0 - (-4)} = \frac{1}{4} \] - **Equation:** \[ y = \frac{1}{4}x - 3 \] --- **7)** Through: \( (-1, -1) \) and \( (-3, 0) \) - **Slope Calculation:** \[ m = \frac{0 - (-1)}{-3 - (-1)} = \frac{1}{-2} = -\frac{1}{2} \] - **Equation:** \[ y = -\frac{1}{2}x - \frac{3}{2} \] --- **9)** Through: \( (-5, 0) \) and \( (-5, -3) \) - **Type:** Vertical Line - **Equation:** \[ x = -5 \] --- **29)** Through: \( (3, -1) \) and \( (-4, -1) \) - **Type:** Horizontal Line - **Equation:** \[ y = -1 \] --- **30)** Through: \( (5, 5) \) and \( (-2, 0) \) - **Slope Calculation:** \[ m = \frac{0 - 5}{-2 - 5} = \frac{-5}{-7} = \frac{5}{7} \] - **Equation:** \[ y = \frac{5}{7}x + \frac{10}{7} \] --- **32)** Through: \( (-4, 2) \) and \( (-2, 1) \) - **Slope Calculation:** \[ m = \frac{1 - 2}{-2 - (-4)} = \frac{-1}{2} = -\frac{1}{2} \] - **Equation:** \[ y = -\frac{1}{2}x \] --- **34)** Through: \( (0, -4) \) and \( (-2, -1) \) - **Slope Calculation:** \[ m = \frac{-1 - (-4)}{-2 - 0} = \frac{3}{-2} = -\frac{3}{2} \] - **Equation:** \[ y = -\frac{3}{2}x - 4 \] --- **36)** Through: \( (0, 1) \) and \( (-2, 5) \) - **Slope Calculation:** \[ m = \frac{5 - 1}{-2 - 0} = \frac{4}{-2} = -2 \] - **Equation:** \[ y = -2x + 1 \] --- **38)** Through: \( (0, 3) \) and \( (-4, 2) \) - **Slope Calculation:** \[ m = \frac{2 - 3}{-4 - 0} = \frac{-1}{-4} = \frac{1}{4} \] - **Equation:** \[ y = \frac{1}{4}x + 3 \] --- **40)** Through: \( (2, 0) \) and \( (-4, 5) \) - **Slope Calculation:** \[ m = \frac{5 - 0}{-4 - 2} = \frac{5}{-6} = -\frac{5}{6} \] - **Equation:** \[ y = -\frac{5}{6}x + \frac{5}{3} \] --- If you need further assistance or explanations on any of these equations, feel free to ask!