To graph the linear equation $-2x + y = 5$ using the point-plotting method, we'll follow these steps:

1. Rearrange the equation to slope-intercept form (y = mx + b): $-2x + y = 5 \quad \Rightarrow \quad y = 2x + 5$ Now the equation is in the form $y = mx + b$, where $m = 2$ (the slope) and $b = 5$ (the y-intercept).

2. Identify the y-intercept: The y-intercept occurs when $x = 0$. So, the point is $(0, 5)$.

3. Use the slope to find another point: The slope $m = 2$ means that for every 1 unit you move to the right (increasing $x$ by 1), you move 2 units up (increasing $y$ by 2). Starting from the point $(0, 5)$, move 1 unit to the right to $x = 1$, and then move up 2 units to $y = 7$. So, the next point is $(1, 7)$.

4. Plot these points on the graph: Plot the points $(0, 5)$ and $(1, 7)$, and then draw a straight line through them to represent the equation.

If you'd like, I can graph it for you using a tool! Would you like me to do that?