Use the given conditions to write an equation for the line in point-slope form and general form. Passing through \( (5,-6) \) and perpendicular to the line whose equation is \( x-2 y-3=0 \) The equation of the line in point-slope form is (Type an equation. Use integers or fractions for any numbers in the equation.)

The line \( x - 2y - 3 = 0 \) can be rewritten in slope-intercept form, \( y = mx + b \), where \( m \) is the slope. Rearranging gives \( 2y = x - 3 \) or \( y = \frac{1}{2}x - \frac{3}{2} \). The slope of this line is \( \frac{1}{2} \). A line that is perpendicular will have a slope that is the negative reciprocal, so the slope of the new line will be \( -2 \). Using point-slope form, we can substitute the slope and the point \( (5, -6) \): \( y - (-6) = -2(x - 5) \) This simplifies to: \( y + 6 = -2x + 10 \) For general form, we can rearrange the equation to: \( 2x + y - 4 = 0 \) So, the equation of the line in point-slope form is: \( y + 6 = -2(x - 5) \) And in general form, it is: \( 2x + y - 4 = 0 \)