Question

What is the slope of a vertical line?

Answer 1

Hint: Here in this question, we have to tell what is the slope value of the vertical line. vertical lines have NO SLOPE. We can't divide by zero, which is of course why this slope value is "undefined". This relationship is always true: a vertical line will have no slope, and "the slope is undefined" or "the line has no slope" means that the line is vertical.

Complete step by step solution:
The slope of a vertical line is infinite or undefined as it has no y-intercept. The slope of a vertical line is undefined. That’s because, in a horizontal line, the change in the x-value will always be 0. You can figure this out by calculating the horizontal difference between the two x-coordinates. Remember the slope formula:
\[\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
With a vertical line, this results in a bottom denominator of 0. However, dividing by 0 is something that doesn’t exist in math! Even though the difference in y-coordinate may change, dividing any number by the change in x-coordinate, 0, will result in an undefined slope.

Hence, The slope of the Verticals lines is undefined.

Note: When graphing linear equations, remember that m, the slope, is calculated by finding the vertical change between two points divided by the horizontal change between those two points.
However, remember these two unique cases: Horizontal lines have a slope of 0 because the vertical change is 0. Vertical lines have an undefined slope because the horizontal change is 0 - we cannot divide a number by 0.