1. **State the problem:** Find the slope of the line passing through the points $(-21, 1)$ and $(49, 97)$. 2. **Formula for slope:** 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. **Substitute the given points:** $$m = \frac{97 - 1}{49 - (-21)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{96}{49 + 21}$$ 5. **Add the denominator terms:** $$m = \frac{96}{70}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (2):** $$m = \frac{\cancel{96}^ {48}}{\cancel{70}^{35}}$$ 7. **Final simplified slope:** $$m = \frac{48}{35}$$ The slope of the line passing through the points $(-21, 1)$ and $(49, 97)$ is $\frac{48}{35}$.