Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through \( (-3,-7) \) and parallel to the line whose equation is \( y=-4 x+3 \) Write an equation for the line in point-slope form. \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. \( \square \) Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the equation of the line that passes through the point \((-3, -7)\) and is parallel to the line \(y = -4x + 3\), follow these steps: ### 1. Determine the Slope Since the lines are parallel, they have the **same slope**. The given line \(y = -4x + 3\) has a slope (\(m\)) of \(-4\). ### 2. Point-Slope Form The **point-slope form** of a line is: \[ y - y_1 = m(x - x_1) \] Where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Using the point \((-3, -7)\) and the slope \(-4\): \[ y - (-7) = -4(x - (-3)) \] Simplify: \[ y + 7 = -4(x + 3) \] **Point-Slope Form:** \[ y + 7 = -4(x + 3) \] ### 3. Slope-Intercept Form The **slope-intercept form** of a line is: \[ y = mx + b \] Where \(m\) is the slope and \(b\) is the y-intercept. We already know \(m = -4\). To find \(b\), plug in the point \((-3, -7)\): \[ -7 = -4(-3) + b \] \[ -7 = 12 + b \] \[ b = -19 \] **Slope-Intercept Form:** \[ y = -4x - 19 \] ### Final Answers - **Point-Slope Form:** \( y + 7 = -4(x + 3) \) - **Slope-Intercept Form:** \( y = -4\,x - 19 \)