Question: Find an equation of the line perpendicular to the x-axis that passes through the point $(8,-2)$. If possible, write the equation in slope-intercept form.
1. **State the problem:** We need to find the equation of a line perpendicular to the x-axis passing through the point $ (8, -2) $.
2. **Recall the properties:** A line perpendicular to the x-axis is a vertical line.
3. **Equation of vertical line:** Vertical lines have the form $ x = a $, where $ a $ is the x-coordinate of any point on the line.
4. **Apply the point:** Since the line passes through $ (8, -2) $, the equation is $ x = 8 $.
5. **Slope-intercept form:** Vertical lines cannot be expressed in slope-intercept form $ y = mx + b $ because their slope is undefined.
**Final answer:** The equation of the line is $$ x = 8 $$ and it cannot be written in slope-intercept form.