Use the given conditions to write an equation for the line in point-slope form and general form Passing through \( (-4,5) \) and parallel to the line whose equation is \( 2 x-9 y-4=0 \) The equation of the line in point-slope form is (Type an equation. Use integers or fractions for any numbers in the equation.) The equation of the line in general form is \( \square=0 \). (Type an expression using \( x \) and \( y \) as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)

To find the equation of the line that passes through the point \((-4, 5)\) and is parallel to the line \(2x - 9y - 4 = 0\), follow these steps: 1. **Determine the Slope of the Given Line:** First, rewrite the given line in slope-intercept form (\(y = mx + b\)) to find its slope: \[ 2x - 9y - 4 = 0 \\ -9y = -2x + 4 \\ y = \frac{2}{9}x - \frac{4}{9} \] The slope (\(m\)) of the given line is \(\frac{2}{9}\). 2. **Use the Point-Slope Form:** Since the desired line is parallel to the given line, it has the same slope. Using the point-slope form \(y - y_1 = m(x - x_1)\) with point \((-4, 5)\) and slope \(\frac{2}{9}\): \[ y - 5 = \frac{2}{9}(x - (-4)) \\ y - 5 = \frac{2}{9}(x + 4) \] **Point-Slope Form:** \[ y - 5 = \frac{2}{9}(x + 4) \] 3. **Convert to General Form:** To convert the equation to general form \(Ax + By + C = 0\), follow these steps: \[ y - 5 = \frac{2}{9}(x + 4) \\ 9(y - 5) = 2(x + 4) \quad \text{(Multiply both sides by 9)} \\ 9y - 45 = 2x + 8 \\ 9y - 2x - 53 = 0 \\ \] Typically, the \(x\) term is written first and the coefficients are positive: \[ 2x - 9y + 53 = 0 \] **General Form:** \[ 2x - 9y + 53 = 0 \] **Final Answers:** - **Point-Slope Form:** \( y - 5 = \frac{2}{9}(x + 4) \) - **General Form:** \( 2x - 9y + 53 = 0 \)