To solve the problem, we need to write the equation of a line parallel to the given line $y = -3x - 5$ and passing through the point $(-2, 4)$.

Steps:

1. Identify the slope of the given line:
   The equation of the line is given in slope-intercept form $y = mx + b$, where $m$ is the slope. For the line $y = -3x - 5$, the slope is $m = -3$.

2. Use the point-slope form of the equation of a line:
   The point-slope form is: $y - y_1 = m(x - x_1)$ Here, $m = -3$ (from the given line), and $(x_1, y_1) = (-2, 4)$ (the given point).

3. Substitute the values: $y - 4 = -3(x + 2)$

4. Simplify the equation: Expand and solve for $y$: $y - 4 = -3x - 6$ $y = -3x - 2$

Final Answer:

The equation of the line is: $y = -3x - 2$

Let me know if you want more details, or if you have any other questions!

Here are 5 related questions to deepen understanding:

1. What is the general form of the equation of a line?
2. How would the equation change if the line was perpendicular instead of parallel?
3. How do you find the slope if the line equation is given in standard form?
4. What happens to the equation if the point changes but the slope remains the same?
5. How can you determine if two lines are parallel from their equations?

Tip: Remember, lines are parallel if they have the same slope.