\[ \text { A line has this equation: } y=-2 x-9 \] Write an equation for the parallel line that goes through \( (3,-5) \).

To find the equation of a line parallel to \( y = -2x - 9 \) that passes through the point \( (3, -5) \), follow these steps: 1. **Determine the slope of the original line:** The given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. For \( y = -2x - 9 \), the slope \( m = -2 \). 2. **Use the same slope for the parallel line:** Parallel lines have identical slopes. Therefore, the slope of the new line is also \( -2 \). 3. **Apply the point-slope form:** The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Plugging in the slope \( m = -2 \) and the point \( (3, -5) \): \[ y - (-5) = -2(x - 3) \] Simplify: \[ y + 5 = -2x + 6 \] \[ y = -2x + 1 \] **Final Equation:** \[ y = -2x + 1 \]