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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
4 hours ago

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: \[ \boxed{y = -1x - 2} \]