Question

select all of the following equations that are equivalent to y=-x-1

Answer 1

To determine which equations are equivalent to \( y = -x - 1 \), we can manipulate this equation or rewrite it in different forms. Here are a few forms to consider:

1. **Standard Form**: If we rearrange the terms, we can write it in standard form \( Ax + By + C = 0 \):
\[
x + y + 1 = 0
\]
or
\[
x + y = -1
\]

2. **Slope-Intercept Form**: The original equation \( y = -x - 1 \) is already in slope-intercept form \( y = mx + b \) where \( m = -1 \) and \( b = -1 \).

3. **Point-Slope Form**: If we know a point on the line (for instance, the point \((-1, 0)\)), we could use the point-slope form. The equation using the point \((-1, 0)\) could be:
\[
y - 0 = -1(x + 1)
\]
Simplifying this gives:
\[
y = -x - 1
\]

4. **Any transformed equations**:
- Multiply both sides by a non-zero constant (e.g., \(2\)):
\[
2y = -2x - 2
\]
- Add or subtract the same value from both sides (e.g., add \(3\)):
\[
y + 3 = -x + 2
\]

These are examples of equivalent forms of the equation. To decide if a given list of equations is equivalent to \( y = -x - 1 \), substitute or rearrange them as needed to see if they result in the same expression.

If you have specific equations to check, feel free to share them, and I can help identify which ones are equivalent!