1. The problem is to analyze the function given by the equation $y = -2x + 2$. 2. This is a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -2$ and the y-intercept $b = 2$. 4. The slope $-2$ means the line decreases by 2 units in $y$ for every 1 unit increase in $x$. 5. The y-intercept $2$ means the line crosses the y-axis at the point $(0, 2)$. 6. To find the x-intercept, set $y = 0$ and solve for $x$: $$0 = -2x + 2$$ $$2x = 2$$ $$x = \cancel{\frac{2}{2}}1$$ 7. So, the x-intercept is at $(1, 0)$. 8. The line has no extrema (no maximum or minimum points) because it is linear. 9. Summary: slope $-2$, y-intercept $(0, 2)$, x-intercept $(1, 0)$, and the graph is a straight line decreasing from left to right.