Question: Write an equation in slope-intercept form for the graph shown.
Line with negative slope passing through the points $(0, -1)$ and $(2, -3)$, extending from top-left to bottom-right; position_hint = center.
1. **State the problem:** Find the equation of the line passing through points $(0, -1)$ and $(2, -3)$ in slope-intercept form $y = mx + b$.
2. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-1)}{2 - 0} = \frac{-3 + 1}{2} = \frac{-2}{2} = -1$$
3. **Use the slope-intercept form $y = mx + b$:**
We know $m = -1$ and the line passes through $(0, -1)$, so $b$ is the $y$-intercept.
4. **Find $b$ by substituting $(0, -1)$:**
$$-1 = -1 \times 0 + b \implies b = -1$$
5. **Write the final equation:**
$$y = -1x - 1$$
Or simply:
$$y = -x - 1$$