What is the equation of the line perpendicular to \( y=\frac{-1}{5} x-25 \) that passes through the point \( (-2,-4) \) ?

To find the equation of the line perpendicular to \( y = \frac{-1}{5} x - 25 \), we first need to determine the slope of the given line. The slope is \( \frac{-1}{5} \). The slope of a line perpendicular to this will be the negative reciprocal, which is \( 5 \). Now, using the point-slope form of the equation of a line, which is given by \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through, we can plug in our values. Here, \( m = 5 \) and the point is \( (-2, -4) \). Substituting in the values, we have: \[ y - (-4) = 5(x - (-2)) \] This simplifies to: \[ y + 4 = 5(x + 2) \] Now distributing the \( 5 \): \[ y + 4 = 5x + 10 \] Next, we solve for \( y \): \[ y = 5x + 10 - 4 \] This gives us the final equation of the line: \[ y = 5x + 6 \]