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To solve the problem, we need to simplify the given equation \( y - 5 = -2(x + 4) \) and then compare it to the options provided.

### Step 1: Simplify the equation
Start by distributing the \(-2\) on the right-hand side:

\[
y - 5 = -2(x + 4)
\]

\[
y - 5 = -2x - 8
\]

### Step 2: Isolate \(y\)
Add 5 to both sides to solve for \(y\):

\[
y = -2x - 8 + 5
\]

\[
y = -2x - 3
\]

### Conclusion:
The equation \(y = -2x - 3\) matches option **D**.

So, the correct answer is **D**.

Would you like a detailed breakdown of any part of the solution, or do you have any other questions?

Here are five related questions you might find interesting:
1. How do you find the slope of a line from an equation?
2. What is the point-slope form of a line, and how is it used?
3. How do you convert between point-slope form and slope-intercept form?
4. What are parallel lines, and how can you identify them by their equations?
5. How does changing the slope or y-intercept of a line affect its graph?

**Tip:** Always remember to distribute any multiplication across terms within parentheses before simplifying the rest of the equation.

Which equation describes the same line as y - 5 = -2(x + 4)?

Learn how to simplify the linear equation y - 5 = -2(x + 4) and match it to one of the provided options. This problem covers the distributive property and slope-intercept form, making it ideal for students in Grades 8-10.

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