Question

Identify the ture statement comparing equations x+y=-1 and x-y=-1.
A. the equations have the same y-interscept
B. the equations have the same slope and y intercept
C. the equations have the same slope
D. the equations have neither the same slope nor the same y intercept

Answer 1

To compare the given equations \( x + y = -1 \) and \( x - y = -1 \), we will rewrite both in slope-intercept form (i.e., \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept).

1. **For the equation \( x + y = -1 \)**:
\[
y = -x - 1
\]
Here, the slope \( m = -1 \) and the y-intercept \( b = -1 \).

2. **For the equation \( x - y = -1 \)**:
\[
-y = -x - 1 \quad \text{ (subtracting \( x \) from both sides)}
\]
\[
y = x + 1
\]
Here, the slope \( m = 1 \) and the y-intercept \( b = 1 \).

Now, we can analyze the statements based on these findings:

- The slopes of the equations are \(-1\) (first equation) and \(1\) (second equation). Therefore, they do not have the same slope.
- The y-intercepts are \(-1\) (first equation) and \(1\) (second equation). Therefore, they do not have the same y-intercept.

Given this analysis, the correct answer is:

**D. the equations have neither the same slope nor the same y intercept.**