What is the gradient of a vertical line?

What is the gradient of a vertical line?

• A. 0
• B. Undefined
• C. 1
• D. Negative one

Answer: (B)

The gradient, or slope, of a line is defined as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). For a vertical line, the change in the horizontal direction is zero because the line does not move left or right; it only extends vertically. When attempting to calculate the gradient of a vertical line, you would have a division by zero scenario since the run (denominator) is zero. In mathematics, division by zero is undefined. Therefore, the gradient of a vertical line is considered to be undefined. This concept can also be visualized: while a horizontal line has a gradient of zero (no rise), a vertical line does not make sense in terms of slope since it does not have any horizontal movement. Hence, calling its gradient "undefined" accurately reflects its behavior.

The gradient, or slope, of a line is defined as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). For a vertical line, the change in the horizontal direction is zero because the line does not move left or right; it only extends vertically.

When attempting to calculate the gradient of a vertical line, you would have a division by zero scenario since the run (denominator) is zero. In mathematics, division by zero is undefined. Therefore, the gradient of a vertical line is considered to be undefined.

This concept can also be visualized: while a horizontal line has a gradient of zero (no rise), a vertical line does not make sense in terms of slope since it does not have any horizontal movement. Hence, calling its gradient "undefined" accurately reflects its behavior.