Question

How do I find if a slope is defined?

Answer 1

examples?

Answer 2

The slope is defined as long as the line isn't vertical. If two points have the same x-coordinate, the slope isn't defined.

Answer 3

The slope of a straight line is defined as the ratio of of the change in y-coordinate, to the change in x-coordinate:
\[m = \frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}\]

As @peachpi points out, if \(x_2\) is the same value as \(x_1\), the fraction get a zero in the denominator. A fraction with a zero in the denominator is not mathematically equal to any number, meaning the slope would be undefined in this case.

Answer 4

This is an example of an undefined slope.