1. The problem is to analyze the equation $y = -x + 1$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -1$ and the y-intercept $b = 1$. 4. The slope $-1$ means the line decreases by 1 unit in $y$ for every 1 unit increase in $x$. 5. The y-intercept $1$ means the line crosses the y-axis at the point $(0,1)$. 6. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = -x + 1 \implies x = 1$$ So the x-intercept is at $(1,0)$. 7. The line passes through points $(0,1)$ and $(1,0)$ and has a negative slope. 8. This information fully describes the line $y = -x + 1$.