Current Skill A line has this equation: \( y=\frac{1}{6} x+3 \) Write an equation for the perpendicular line that goes through \( (-5,8) \).

To find the equation of the line perpendicular to \( y = \frac{1}{6}x + 3 \) that passes through the point \( (-5, 8) \), follow these steps: 1. **Determine the slope of the given line:** The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. \[ m_1 = \frac{1}{6} \] 2. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. \[ m_2 = -\frac{1}{m_1} = -6 \] 3. **Use the point-slope form to find the equation:** The point-slope form is: \[ y - y_1 = m(x - x_1) \] Substituting \( m = -6 \) and the point \( (-5, 8) \): \[ y - 8 = -6(x - (-5)) \] \[ y - 8 = -6(x + 5) \] 4. **Simplify to slope-intercept form:** \[ y - 8 = -6x - 30 \] \[ y = -6x - 22 \] **Final Answer:** \[ y = -6x - 22 \]