Consider the line $$ -x-8 y=8 $$. Find the equation of the line that is parallel to this line and passes through the point $$ (3,-3) $$. Find the equation of the line that is perpendicular to this line and passes through the point $$ (3,-3) $$. Equation of parallel line:

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To find the equation of the line parallel to $$ -x - 8y = 8 $$ that passes through the point $$ (3, -3) $$, follow these steps:

1. **Determine the Slope of the Original Line:**

Rewrite the original equation in slope-intercept form ($$ y = mx + b $$) to identify the slope.

$$
   -x - 8y = 8 \
   -8y = x + 8 \
   y = -\frac{1}{8}x - 1
   $$

The slope ($$ m $$) of the original line is $$ -\frac{1}{8} $$.

2. **Use the Slope for the Parallel Line:**

Parallel lines have the same slope. Therefore, the slope of the new line is also $$ -\frac{1}{8} $$.

3. **Apply the Point-Slope Form:**

Use the point $$ (3, -3) $$ to find the equation of the parallel line.

$$
   y - y_1 = m(x - x_1) \
   y - (-3) = -\frac{1}{8}(x - 3) \
   y + 3 = -\frac{1}{8}x + \frac{3}{8} \
   y = -\frac{1}{8}x + \frac{3}{8} - 3 \
   y = -\frac{1}{8}x - \frac{21}{8}
   $$

4. **Convert to Standard Form (Optional):**

To express the equation in a form similar to the original:

$$
   y = -\frac{1}{8}x - \frac{21}{8} \
   8y = -x - 21 \
   -x - 8y = 21
   $$

Multiplying both sides by $$ -1 $$ for a cleaner appearance:

$$
   x + 8y = -21
   $$

**Final Answer:**

$$ -x - 8y = 21 $$
The equation of the parallel line is $$ -x - 8y = 21 $$.

Consider the line .
Find the equation of the line that is parallel to this line and passes through the point .
Find the equation of the line that is perpendicular to this line and passes through the point .
Equation of parallel line:

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Consider the line . Find the equation of the line that is parallel to this line and passes through the point . Find the equation of the line that is perpendicular to this line and passes through the point . Equation of parallel line: