Which of the following equations defines a line that is parallel to the line $$ y=-\frac{4}{3} x-4 $$ and passes through the point $$ (3,-1) $$ ? A $$ y=-\frac{4}{3} x-1 $$ B $$ y=-\frac{4}{3} x-3 $$ C $$ y=-\frac{4}{3} x+1 $$ D $$ y=-\frac{4}{3} x+3 $$

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To find the equation of a line that is parallel to the given line and passes through a specific point, follow these steps:

1. **Identify the Slope of the Given Line:**
   
   The given line is $$ y = -\frac{4}{3}x - 4 $$. The slope ($$ m $$) of this line is $$-\frac{4}{3}$$.

2. **Formulate the Equation of the Parallel Line:**
   
   Since parallel lines have the same slope, the equation of the desired line will also have a slope of $$-\frac{4}{3}$$. Thus, the equation will be of the form:
   $$
   y = -\frac{4}{3}x + b
   $$
   where $$ b $$ is the y-intercept we need to determine.

3. **Use the Given Point to Find $$ b $$:**
   
   The line must pass through the point $$ (3, -1) $$. Substitute $$ x = 3 $$ and $$ y = -1 $$ into the equation:
   $$
   -1 = -\frac{4}{3}(3) + b
   $$
   Simplifying:
   $$
   -1 = -4 + b \implies b = -1 + 4 \implies b = 3
   $$

4. **Write the Final Equation:**
   
   Substituting $$ b = 3 $$ back into the equation:
   $$
   y = -\frac{4}{3}x + 3
   $$

**Answer:**  
**D** $$ y=-\frac{4}{3} x+3 $$
The equation of the line parallel to $$ y = -\frac{4}{3}x - 4 $$ that passes through $$ (3, -1) $$ is $$ y = -\frac{4}{3}x + 3 $$.

Which of the following equations defines a line that is parallel to the line and
passes through the point ?
A
B
C
D

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Which of the following equations defines a line that is parallel to the line and passes through the point ? A B C D