1. **State the problem:** Find the equation of the line passing through the points $(-4,7)$ and $(-4,-3)$. 2. **Formula used:** The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. The point-slope form of a line is $y - y_1 = m(x - x_1)$. 3. **Calculate the slope:** Here, $x_1 = -4$, $y_1 = 7$, $x_2 = -4$, $y_2 = -3$. $$m = \frac{-3 - 7}{-4 - (-4)} = \frac{-10}{0}$$ Since division by zero is undefined, the slope is undefined, meaning the line is vertical. 4. **Equation of the line:** For a vertical line passing through $x = -4$, the equation is simply $$x = -4$$ This line passes through both points and has an undefined slope. **Final answer:** The equation of the line is $x = -4$.