To find which equation describes the same line as \( y - 3 = -1(x + 5) \), we first need to simplify the given equation into the slope-intercept form (i.e., \( y = mx + b \)).
Starting with: \[ y - 3 = -1(x + 5) \]
Distributing the \(-1\) on the right side: \[ y - 3 = -1x - 5 \]
Next, add 3 to both sides: \[ y = -1x - 5 + 3 \] \[ y = -1x - 2 \]
Now we have the line in the form \( y = -1x - 2 \).
Now, let's compare this with the options given:
- \( y = -1x + 8 \) (not the same)
- \( y = -1x - 5 \) (not the same)
- \( y = -1x - 2 \) (this matches)
- \( y = -1x - 1 \) (not the same)
The equation that describes the same line as \( y - 3 = -1(x + 5) \) is: \[ \boxed{y = -1x - 2} \]