1. **Stating the problem:** We have multiple linear equations given, and we want to understand and analyze them. 2. **Equations given:** - $y = -1 \cdot x + 3$ - $y = -1 \cdot x - 2$ - $x = y - 1$ - $y = 2$ - $y = -1 \cdot (x - 1)$ - $y = -2$ - $y = x + 1$ 3. **Understanding each equation:** - Equations like $y = mx + b$ represent lines with slope $m$ and y-intercept $b$. - $x = y - 1$ can be rewritten as $y = x + 1$. - Horizontal lines have the form $y = c$ where $c$ is constant. 4. **Rewrite and simplify where needed:** - $x = y - 1 \implies y = x + 1$ - $y = -1 \cdot (x - 1) = -x + 1$ 5. **Summary of lines:** - $y = -x + 3$ - $y = -x - 2$ - $y = x + 1$ - $y = 2$ - $y = -x + 1$ - $y = -2$ - $y = x + 1$ (repeated) 6. **Interpretation:** - These are straight lines with different slopes and intercepts. - Some lines are parallel (same slope), e.g., $y = -x + 3$ and $y = -x - 2$. - Some are horizontal lines, e.g., $y = 2$ and $y = -2$. 7. **Final note:** Each equation represents a line on the coordinate plane, and understanding their slopes and intercepts helps graph and analyze their intersections.