Sure, let's solve this step by step.
First, we need to convert the given equation [tex]\( y - 5 = -2(x + 4) \)[/tex] into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex].
1. Start with the original equation:
[tex]\[ y - 5 = -2(x + 4) \][/tex]
2. Distribute the [tex]\(-2\)[/tex] on the right-hand side:
[tex]\[ y - 5 = -2x - 8 \][/tex]
3. Isolate [tex]\( y \)[/tex] by adding 5 to both sides:
[tex]\[ y = -2x - 8 + 5 \][/tex]
4. Simplify the equation:
[tex]\[ y = -2x - 3 \][/tex]
Now we have the equation in slope-intercept form [tex]\[ y = -2x - 3 \][/tex].
Next, we compare this with the given options:
- Option A: [tex]\( y = -2x + 9 \)[/tex]
- Option B: [tex]\( y = -2x - 2 \)[/tex]
- Option C: [tex]\( y = -2x - 3 \)[/tex]
- Option D: [tex]\( y = -2x - 8 \)[/tex]
From these options, we see that the equation [tex]\( y = -2x - 3 \)[/tex] matches Option C.
Therefore, the equation that describes the same line as [tex]\( y - 5 = -2(x + 4) \)[/tex] is [tex]\[ \boxed{y = -2x - 3} \][/tex].
Hence, the correct answer is Option C.
