Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through \( (-5,-4) \) and parallel to the line whose equation is \( y=-5 x+1 \) Write an equation for the line in point-slope form. Write an equation for the line in slope-intercept form. (Simplify your answer. Use integers or fractions for any numbers in the equation.) (Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the equation of a line that passes through the point \((-5, -4)\) and is parallel to the line \(y = -5x + 1\), we'll follow these steps: 1. **Determine the slope of the given line.** 2. **Use the point-slope form to write the equation of the new line.** 3. **Convert the point-slope form to slope-intercept form.** ### 1. Determine the Slope The given line is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope. \[ y = -5x + 1 \quad \Rightarrow \quad \text{Slope} \, (m) = -5 \] Since parallel lines have the same slope, the slope of the new line is also \(-5\). ### 2. Point-Slope Form The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Where: - \(m\) is the slope. - \((x_1, y_1)\) is a point on the line. Plugging in the values: \[ y - (-4) = -5(x - (-5)) \] \[ y + 4 = -5(x + 5) \] **Point-Slope Form:** \[ y + 4 = -5(x + 5) \] ### 3. Slope-Intercept Form To convert the point-slope form to slope-intercept form (\(y = mx + b\)), we'll simplify the equation: \[ y + 4 = -5(x + 5) \] \[ y + 4 = -5x - 25 \] \[ y = -5x - 25 - 4 \] \[ y = -5x - 29 \] **Slope-Intercept Form:** \[ y = -5x - 29 \] ### Final Answer - **Point-Slope Form:** \( y + 4 = -5(x + 5) \) - **Slope-Intercept Form:** \( y = -5x - 29 \)