To determine which equation describes the same line as the given equation \( y - 3 = -1(x + 5) \), we will start by transforming the given equation into a more standard form, specifically the slope-intercept form \( y = mx + b \).
1. Start with the given equation:
[tex]\[
y - 3 = -1(x + 5)
\][/tex]
2. Distribute the \(-1\) on the right side:
[tex]\[
y - 3 = -x - 5
\][/tex]
3. Add \( 3 \) to both sides of the equation to isolate \( y \):
[tex]\[
y = -x - 5 + 3
\][/tex]
4. Simplify the right side:
[tex]\[
y = -x - 2
\][/tex]
The resulting equation is \( y = -x - 2 \).
Now, let's compare this equation with the given options:
A. \( y = -1x - 1 \)
B. \( y = -1x + 8 \)
C. \( y = -1x - 2 \)
D. \( y = -1x - 5 \)
The equation \( y = -x - 2 \) matches option C.
Therefore, the equation that describes the same line as \( y - 3 = -1(x + 5) \) is:
C. [tex]\( y = -1 x - 2 \)[/tex]
