Question: What is the equation of the line that goes through $(0, 2)$ and is parallel to $y=-2x-1$?
1. **State the problem:** Find the equation of the line passing through the point $(0, 2)$ and parallel to the line $y = -2x - 1$.
2. **Recall the formula:** The equation of a line in point-slope form is $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
3. **Identify the slope:** Since the line must be parallel to $y = -2x - 1$, it has the same slope $m = -2$.
4. **Plug in the point and slope:** Using $(x_1, y_1) = (0, 2)$ and $m = -2$, the equation is:
$$y - 2 = -2(x - 0)$$
5. **Simplify the equation:**
$$y - 2 = -2x$$
6. **Isolate $y$ to get slope-intercept form:**
$$y = -2x + 2$$
**Final answer:** The equation of the line is $$y = -2x + 2$$.