Questions: Select the answer that best completes the given statement. The slope of a vertical line is negative. undefined. positive. zero. one.

Solution Steps

To determine the slope of a vertical line, we need to understand that a vertical line has an undefined slope because the change in x (horizontal change) is zero, which would make the denominator of the slope formula zero, leading to an undefined value.

The slope of a line is calculated using the formula:

\[ m = \frac{\Delta y}{\Delta x} \]

where \( \Delta y \) is the change in the y-coordinates and \( \Delta x \) is the change in the x-coordinates. For a vertical line, all points on the line have the same x-coordinate, which means \( \Delta x = 0 \).

When \( \Delta x = 0 \), the slope formula becomes:

\[ m = \frac{\Delta y}{0} \]

Division by zero is undefined in mathematics, which means the slope of a vertical line is undefined.

Final Answer