Vertical Lines 3B15A8

1. **State the problem:** We need to determine which statement about vertical lines is true. 2. **Recall the definition of slope:** The slope $m$ of a line is given by the formula $$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. 3. **Analyze vertical lines:** For a vertical line, all points have the same $x$-coordinate, so $$x_1 = x_2$$ 4. **Calculate the slope for vertical lines:** Substituting into the slope formula, $$m = \frac{y_2 - y_1}{\cancel{x_2 - x_1}}$$ Since $x_2 - x_1 = 0$, the denominator is zero, which means the slope is undefined. 5. **Check the coordinates:** Because the $x$-coordinate is constant for all points on a vertical line, all $x$-coordinates are the same. 6. **Conclusion:** The true statement is: "Vertical lines have an undefined slope and all of the $x$-coordinates are the same."