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.)

1. The given line is \( x-9y-4=0 \). We first rewrite it in slope-intercept form to find its slope. Isolating \( y \): \[ x-9y-4=0 \quad \Rightarrow \quad -9y = -x+4 \quad \Rightarrow \quad y=\frac{1}{9}x-\frac{4}{9} \] Thus, the slope of the given line is \( m_1=\frac{1}{9} \). 2. The line we want to find is perpendicular to the given line. The slope of the perpendicular line is the negative reciprocal of \( \frac{1}{9} \): \[ m_2=-\frac{1}{\frac{1}{9}}=-9 \] 3. We are given that the line passes through the point \( (4,-5) \). Using the point-slope form of a line: \[ y-y_1=m(x-x_1) \] Substitute \( (x_1,y_1)=(4,-5) \) and \( m=-9 \): \[ y-(-5)=-9(x-4) \] This simplifies to: \[ y+5=-9(x-4) \] 4. To write the general form, expand the point-slope equation: \[ y+5=-9x+36 \] Rearrange to get all terms on one side: \[ 9x+y+5-36=0 \quad \Rightarrow \quad 9x+y-31=0 \] Thus, the equations of the line are: - Point-slope form: \( y+5=-9(x-4) \) - General form: \( 9x+y-31=0 \)