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The problem asks for the equation of a line in slope-intercept form, \( y = mx + b \), which passes through the point \( (-5, -7) \) and is parallel to the line given by the equation \( y = -2x + 4 \).

### Steps to solve:

1. **Find the slope (m):** 
   The slope of the given line \( y = -2x + 4 \) is \( m = -2 \). Since the new line is parallel, it will have the same slope, \( m = -2 \).

2. **Use the point-slope form of a line:**
   The point-slope form is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point the line passes through. Here, \( (x_1, y_1) = (-5, -7) \) and \( m = -2 \).

   Substituting these values into the equation:
   \[
   y - (-7) = -2(x - (-5))
   \]
   This simplifies to:
   \[
   y + 7 = -2(x + 5)
   \]

3. **Simplify to slope-intercept form:**
   Now distribute the slope on the right-hand side:
   \[
   y + 7 = -2x - 10
   \]
   Subtract 7 from both sides to isolate \( y \):
   \[
   y = -2x - 17
   \]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -2x - 17
\]

Would you like more details or have any further questions?

Here are some related questions:
1. How do you find the slope when lines are perpendicular?
2. What changes when the problem asks for a perpendicular line instead of a parallel one?
3. Can you solve for the equation of a line given two points?
4. What is the difference between point-slope and slope-intercept form?
5. How do you convert a line equation from standard form to slope-intercept form?

**Tip:** Parallel lines always have the same slope!

Write an equation in slope-intercept form of the line that passes through the point (-5, -7) and is parallel to the graph of the equation y = -2x + 4.

Learn how to find the equation of a line in slope-intercept form that passes through the point (-5, -7) and is parallel to the line y = -2x + 4. This solution includes step-by-step guidance on using the slope of parallel lines and point-slope form. Suitable for students in Grades 8-10.

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