Click here to watch the video. Use the given conditions to write an equation for the line in point-slope form and general form. Passing through \( (4,-5) \) and perpendicular to the line whose equation is \( x-9 y-4=0 \) The equation of the line in point-slope form is (Type an equation. Use integers or fractions for any numbers in the equation.)

To find the equation of the line, we first need to determine the slope of the given line \(x - 9y - 4 = 0\). Rearranging this to slope-intercept form \(y = mx + b\) gives us: \[ 9y = x - 4 \] \[ y = \frac{1}{9}x - \frac{4}{9} \] The slope of this line is \(\frac{1}{9}\). For a line that is perpendicular to this one, the slope will be the negative reciprocal, which is \(-9\). Now, using the point-slope form of the equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the point through which the line passes, we plug in \((4, -5)\) and the slope \(-9\): \[ y - (-5) = -9(x - 4) \] \[ y + 5 = -9(x - 4) \] Thus, the equation in point-slope form is: \[ y + 5 = -9(x - 4) \] For the general form, we can rearrange this to standard form \(Ax + By + C = 0\): \[ y + 5 = -9x + 36 \] \[ 9x + y - 31 = 0 \] Therefore, your final answers are: Point-slope form: \(y + 5 = -9(x - 4)\) General form: \(9x + y - 31 = 0\)