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

Transcript text: Select the answer that best completes the given statement. The slope of a vertical line is $\square$ negative. undefined. positive. zero. one.

Solution

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.

Step 1: Understanding the Slope of a Vertical Line

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 $.

Step 2: Analyzing the Implication of $\Delta x = 0$

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.