## vertical line slope

### The slope of a vertical line is undefined

The slope of a vertical line is undefined. In mathematics, slope is a measure of how steep a line is and is defined as the change in y-coordinates divided by the change in x-coordinates. However, for a vertical line, the x-coordinates do not change, leading to a denominator of zero. Division by zero is undefined in mathematics, so the slope of a vertical line is considered undefined.

Visually, you can imagine a vertical line as a line that is perfectly upright, going straight up or down. Since it does not have any horizontal extent, it does not have an angle of inclination, which is the measure of steepness for non-vertical lines. As a result, a vertical line does not have a defined slope.

Mathematically, we can see this when we try to calculate the slope using the slope formula. Let’s say we have two points on a vertical line, (x1, y1) and (x2, y2). The x-coordinates are the same for both points, so we use the formula:

slope = (y2 – y1) / (x2 – x1)

However, since x2 and x1 are equal, the denominator becomes zero. Therefore, the slope of a vertical line cannot be determined using this formula.

To summarize, the slope of a vertical line is undefined because the change in x-coordinates is zero, leading to division by zero in the slope formula.

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