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The problem in the image is asking for the equation of the line in the general form \( Ax + By + C = 0 \) that passes through the point \((-2, 3)\) and is parallel to a given line.

### Problem Statement:
Find the equation of the line that is in general form \( Ax + By + C = 0 \) and passes through the point \((-2, 3)\) and is parallel to the line \( -2y = 3x - 8 \).

### Solution:
1. **Find the slope of the given line:**

   The equation of the given line is \( -2y = 3x - 8 \). First, we'll rewrite this equation in slope-intercept form \( y = mx + b \).

   \[
   -2y = 3x - 8
   \]

   Divide the entire equation by \(-2\):

   \[
   y = -\frac{3}{2}x + 4
   \]

   Here, the slope \( m \) of the given line is \( -\frac{3}{2} \).

2. **Write the equation of the line parallel to the given line:**

   Since the lines are parallel, they will have the same slope. The slope of our required line is also \( -\frac{3}{2} \).

   Using the point-slope form \( y - y_1 = m(x - x_1) \), where \((x_1, y_1)\) is the point \((-2, 3)\), we have:

   \[
   y - 3 = -\frac{3}{2}(x + 2)
   \]

3. **Simplify and convert to general form:**

   Expand and simplify the equation:

   \[
   y - 3 = -\frac{3}{2}x - 3
   \]

   Add 3 to both sides:

   \[
   y = -\frac{3}{2}x
   \]

   Multiply the entire equation by 2 to eliminate the fraction:

   \[
   2y = -3x
   \]

   Finally, rearrange the terms to get the general form \( Ax + By + C = 0 \):

   \[
   3x + 2y = 0
   \]

### Final Answer:
The equation of the line in general form that passes through \((-2, 3)\) and is parallel to the given line is \( 3x + 2y = 0 \).

Would you like any more details or have any questions?

Here are five related questions you might find interesting:
1. How do you find the equation of a line given two points?
2. What is the difference between the general form and slope-intercept form of a line?
3. How do you determine if two lines are perpendicular?
4. Can you derive the equation of a line from its graph?
5. What is the significance of the coefficients in the general form of a line's equation?

**Tip:** When dealing with parallel lines, always remember that they share the same slope. This fact simplifies the process of finding their equations.

Find the equation of the line in general form Ax + By + C = 0 that passes through the point (-2, 3) and is parallel to the line -2y = 3x - 8.

Learn how to find the equation of a line in general form Ax + By + C = 0 that passes through (-2, 3) and is parallel to the line -2y = 3x - 8. This problem involves understanding the slope of parallel lines, point-slope form, and converting to general form.

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