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

To find the equation of a line that is parallel to \( y = -2x - 9 \) and passes through the point \( (3, -5) \), we start by noting that parallel lines have the same slope. The slope from the original line is \(-2\). Now, we can use the point-slope form of a linear equation: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope, and \( (x_1, y_1) \) is the point on the line. Plugging in the values \( m = -2 \), \( x_1 = 3 \), and \( y_1 = -5\): \[ y - (-5) = -2(x - 3) \] This simplifies to: \[ y + 5 = -2x + 6 \] Subtracting 5 from both sides gives: \[ y = -2x + 1 \] Thus, the equation of the parallel line that goes through \( (3, -5) \) is: \[ y = -2x + 1 \]