Question

Which equation describes the same line as y - 3 = -1(x + 5)?
0 y=-1x+ 8
О у = -1х - 5
Oy=-1х - 2
O y =-1x-1

Answers

Answered by GPT-4o mini
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:

1. \( y = -1x + 8 \) (not the same)
2. \( y = -1x - 5 \) (not the same)
3. \( y = -1x - 2 \) (this matches)
4. \( y = -1x - 1 \) (not the same)

The equation that describes the same line as \( y - 3 = -1(x + 5) \) is:
\[
\boxed{y = -1x - 2}
\]

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