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!