1. **State the problem:** We need to find the value of $t$ for a line passing through points $(0, -4)$ and $(t, -3)$ with a slope of 1. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula:** Using points $(0, -4)$ and $(t, -3)$, $$1 = \frac{-3 - (-4)}{t - 0} = \frac{-3 + 4}{t} = \frac{1}{t}$$ 4. **Solve for $t$:** $$1 = \frac{1}{t}$$ Multiply both sides by $t$: $$t \times 1 = t \times \frac{1}{t}$$ $$t = \cancel{t} \times \frac{1}{\cancel{t}} = 1$$ 5. **Final answer:** $$\boxed{1}$$