1. **State the problem:** Find the slope of the line passing through the points $(-3,-7)$ and $(3,7)$. 2. **Formula for slope:** The slope $m$ of a line through 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 points:** $$m=\frac{7 - (-7)}{3 - (-3)}$$ 4. **Simplify the numerator and denominator:** $$m=\frac{7 + 7}{3 + 3}$$ 5. **Calculate sums:** $$m=\frac{14}{6}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2:** $$m=\frac{\cancel{14}^7}{\cancel{6}^3}$$ 7. **Final slope:** $$m=\frac{7}{3}$$ **Answer:** The slope of the line is $\frac{7}{3}$.