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]



Answer :

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]