through: \( (-1,0) \), perp. to \( y=-x-4 \)

To find the equation of the line that is **perpendicular** to \( y = -x - 4 \) and **passes through** the point \( (-1, 0) \), follow these steps: ### 1. Determine the Slope of the Given Line The given equation is in the **slope-intercept form**: \[ y = mx + b \] where: - \( m \) is the **slope**, - \( b \) is the **y-intercept**. For \( y = -x - 4 \): \[ m_1 = -1 \] ### 2. Find the Slope of the Perpendicular Line Lines that are perpendicular to each other have slopes that are **negative reciprocals**. \[ m_2 = -\frac{1}{m_1} = -\frac{1}{-1} = 1 \] So, the slope of the perpendicular line is \( m_2 = 1 \). ### 3. Use the Point-Slope Form to Find the Equation 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, - \( m \) is the slope. Given the point \( (-1, 0) \) and slope \( m_2 = 1 \): \[ y - 0 = 1(x - (-1)) \] \[ y = 1(x + 1) \] \[ y = x + 1 \] ### **Final Answer** The equation of the line **perpendicular** to \( y = -x - 4 \) and **passing through** the point \( (-1, 0) \) is: \[ \boxed{y = x + 1} \]