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The problem in the image asks to write the equation of a line parallel to the line \( 2x + y = 3 \) and passing through the point (-2, 5).

### Steps to solve:

1. **Find the slope of the given line**:
   The given line is \( 2x + y = 3 \). We can rewrite it in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

   \[
   y = -2x + 3
   \]

   So, the slope of the line is \( m = -2 \).

2. **Use the same slope for the parallel line**:
   Lines that are parallel have the same slope. Therefore, the line we need to find will also have a slope of \( -2 \).

3. **Use the point-slope form of a line**:
   The point-slope form of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope. In this case, the point is \( (-2, 5) \) and the slope \( m = -2 \).

   Substituting the values:
   \[
   y - 5 = -2(x + 2)
   \]

4. **Simplify the equation**:
   Expanding and simplifying the equation:
   \[
   y - 5 = -2x - 4
   \]
   \[
   y = -2x + 1
   \]

So, the equation of the line parallel to \( 2x + y = 3 \) and passing through \( (-2, 5) \) is:
\[
y = -2x + 1
\]

Would you like any further details or explanations?

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### 5 Related Questions:
1. What is the slope of a line perpendicular to \( 2x + y = 3 \)?
2. How do you convert a line equation from standard form to slope-intercept form?
3. What is the point-slope form, and when is it used?
4. How do you write the equation of a line perpendicular to another line?
5. How do you determine if two lines are parallel or perpendicular?

### Tip:
When given a line equation in standard form, always rearrange it into slope-intercept form to easily identify the slope for parallel or perpendicular line problems.

Write a line parallel to the line 2x + y = 3 and passes through the point (-2, 5).

Learn how to find the equation of a line parallel to 2x + y = 3 that passes through the point (-2, 5). This problem explores linear equations, the slope-intercept form, and parallel lines, ideal for students in Grades 8-10.

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