 Find the equation of the line that is parallel to: y = −5  -x/2and passes through ( 1− ,6) 

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.

Find the equation of the line that is parallel to: y = −5 - x/2 and passes through (1, −6)

Discover how to find the equation of a line parallel to y = −5 - x/2 and passing through the point (1, −6). This guide explains key concepts such as slope-intercept form, point-slope form, and parallel line properties. Ideal for students in Grades 8-10.

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