1. The problem is to identify the graph of the linear function $y = -2x + 3$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. For $y = -2x + 3$, the slope $m = -2$ and the y-intercept $b = 3$. 4. The slope $-2$ means the line goes down 2 units for every 1 unit it moves to the right. 5. The y-intercept $3$ means the line crosses the y-axis at $(0, 3)$. 6. Graph A has a positive slope approximately $+2$, so it does not match. 7. Graph B has a negative slope approximately $-2$, which matches the slope of our function. 8. Therefore, the correct graph is Graph B.