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To find the equation of line \( q \), we need to consider the following steps:

1. **Identify the slope of line \( p \):**
   The equation of line \( p \) is given as:
   \[
   y = -\frac{1}{4}x - 8
   \]
   Here, the slope (\( m \)) of line \( p \) is \( -\frac{1}{4} \).

2. **Slope of line \( q \):**
   Since line \( q \) is parallel to line \( p \), it will have the same slope. Therefore, the slope of line \( q \) is also \( -\frac{1}{4} \).

3. **Using the point-slope form:**
   Line \( q \) passes through the point \( (6, -3) \) and has a slope of \( -\frac{1}{4} \). The point-slope form of a line's equation is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting \( m = -\frac{1}{4} \) and the point \( (6, -3) \), we have:
   \[
   y - (-3) = -\frac{1}{4}(x - 6)
   \]
   Simplifying:
   \[
   y + 3 = -\frac{1}{4}(x - 6)
   \]
   \[
   y + 3 = -\frac{1}{4}x + \frac{6}{4}
   \]
   \[
   y + 3 = -\frac{1}{4}x + \frac{3}{2}
   \]

4. **Converting to slope-intercept form:**
   To get the equation in slope-intercept form (\( y = mx + b \)), subtract 3 from both sides:
   \[
   y = -\frac{1}{4}x + \frac{3}{2} - 3
   \]
   \[
   y = -\frac{1}{4}x + \frac{3}{2} - \frac{6}{2}
   \]
   \[
   y = -\frac{1}{4}x - \frac{3}{2}
   \]

Hence, the equation of line \( q \) is:
\[
y = -\frac{1}{4}x - \frac{3}{2}
\]

Would you like further details or have any questions?

**Related Questions:**
1. How do you find the slope of a line given its equation in standard form?
2. What is the point-slope form and how is it used to write the equation of a line?
3. Can two lines be parallel if they have different slopes?
4. How do you convert between slope-intercept form and point-slope form?
5. How do you find the equation of a line perpendicular to a given line passing through a point?

**Tip:** Remember that parallel lines always have the same slope, but different \( y \)-intercepts unless they are identical lines.

The equation of line p is y = -(1/4)x - 8. Line q, which is parallel to line p, includes the point (6, -3). What is the equation of line q?

Learn how to find the equation of a line parallel to another line with a slope of -1/4 that passes through the point (6, -3). This problem covers concepts such as slope-intercept form and point-slope form, ideal for students in Grades 8-10.

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