1. **State the problem:** We need to find the equation of a line that passes through the point $(0, 2)$ and is parallel to the line given by $$y = -2x + 5.$$ 2. **Recall the formula and rules:** Lines that are parallel have the same slope. The slope-intercept form of a line is $$y = mx + b,$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify the slope of the given line:** The given line is $$y = -2x + 5,$$ so its slope is $$m = -2.$$ 4. **Use the slope for the new line:** Since the new line is parallel, it must have the same slope $$m = -2.$$ 5. **Find the y-intercept $b$ of the new line:** The new line passes through $(0, 2)$, which means when $x=0$, $y=2$. Substitute into $$y = mx + b$$ to find $b$: $$2 = -2(0) + b \implies b = 2.$$ 6. **Write the equation of the new line:** Using $m = -2$ and $b = 2$, the equation is $$y = -2x + 2.$$ **Final answer:** The equation of the new line is $$y = -2x + 2.$$ This corresponds to option (a).