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The problem asks for the equation of a line parallel to the line \( y + 3 = -5x \) that passes through the point \( (-2, 3) \).

### Step-by-step solution:

1. **Find the slope of the given line:**
   The equation of the given line is:
   \[
   y + 3 = -5x
   \]
   Rearranging it into slope-intercept form \( y = mx + b \), we get:
   \[
   y = -5x - 3
   \]
   Here, the slope \( m \) is \( -5 \).

2. **Use the point-slope form:**
   The line parallel to the given line must have the same slope, which is \( m = -5 \). The point-slope form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) = (-2, 3) \) is the point the line passes through and \( m = -5 \).

3. **Plug in the point and slope:**
   Substituting the values, we get:
   \[
   y - 3 = -5(x + 2)
   \]

4. **Check the answer:**
   The equation matches option **A**: \( y - 3 = -5(x + 2) \).

Thus, the correct answer is **A**.

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Would you like more details or have any questions about this process?

### Related Questions:
1. What is the point-slope form of a line equation?
2. How can you find the slope of a line given two points?
3. What is the difference between parallel and perpendicular lines in terms of their slopes?
4. How do you convert a line equation into slope-intercept form?
5. How would the equation change if the line was perpendicular instead of parallel?

### Tip:
When dealing with lines, remember that parallel lines have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other.

Which of the following is the equation of a line parallel to y + 3 = -5x that passes through the point (-2, 3)?

A. y - 3 = -5(x + 2)
B. y - 3 = \frac{1}{5}(x + 2)
C. y + 3 = \frac{1}{5}(x - 2)
D. y + 3 = 5(x - 2)

Find the equation of a line parallel to y + 3 = -5x that passes through the point (-2, 3). Learn how to use the point-slope form and understand the properties of parallel lines in this algebra problem, suitable for students in Grades 9-11.

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