To find the equation of a line parallel to $y = -5 - \frac{x}{2}$ and passing through $(1, -6)$, follow these steps:

1. Identify the slope of the given line.
   The equation $y = -5 - \frac{x}{2}$ is in slope-intercept form $y = mx + b$, where $m$ is the slope.
   Here, $m = -\frac{1}{2}$.

2. Parallel lines have the same slope.
   Therefore, the slope of our new line is also $-\frac{1}{2}$.

3. Use the point-slope form of a line.
   The point-slope form is $y - y_1 = m(x - x_1)$, where $(x_1, y_1) = (1, -6)$ and $m = -\frac{1}{2}$.
   Substitute the values:
   $y - (-6) = -\frac{1}{2}(x - 1)$ Simplify:
   $y + 6 = -\frac{1}{2}x + \frac{1}{2}$

4. Rewrite in slope-intercept form.
   Subtract 6 from both sides:
   $y = -\frac{1}{2}x + \frac{1}{2} - 6$ Simplify further:
   $y = -\frac{1}{2}x - \frac{11}{2}$

The equation of the line parallel to $y = -5 - \frac{x}{2}$ and passing through $(1, -6)$ is: $y = -\frac{1}{2}x - \frac{11}{2}$

Would you like further details or have any questions?

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Additional Questions

1. How do you find the slope of a line given two points?
2. What is the difference between parallel and perpendicular lines in terms of their slopes?
3. How can you convert a line equation from point-slope form to standard form?
4. What does it mean for two lines to be parallel in a coordinate plane?
5. How would you determine the y-intercept of a line that passes through two points?

Tip

Parallel lines always have the same slope but different y-intercepts.