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Which equation describes the same line as [tex] y - 3 = -1(x + 5) [/tex]?
A. [tex] y = -1x - 1 [/tex] B. [tex] y = -1x + 8 [/tex] C. [tex] y = -1x - 2 [/tex] D. [tex] y = -1x - 5 [/tex]
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:
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