# Thread: Slope of Lines

1. ## Slope of Lines

For years, I have heard that the slope of vertical lines is undefined (does not exist) and the slope of horizontal lines is zero but no clear and/or easy explanation has ever been given by a teacher or professor in my experience.

Why is the slope of vertical lines undefined and at the same time, why is the slope of horizontal lines zero?

2. Originally Posted by magentarita
For years, I have heard that the slope of vertical lines is undefined (does not exist) and the slope of horizontal lines is zero but no clear and/or easy explanation has ever been given by a teacher or professor in my experience.

Why is the slope of vertical lines undefined and at the same time, why is the slope of horizontal lines zero?

Hello magentarita,

Let's just talk about the definition of slope. It's the change in y divided by the change in x.

$\displaystyle slope=\frac{\Delta y}{\Delta x}$

In a vertical line, there is no change in x. It remains constant. Therefore,

$\displaystyle slope=\frac{\Delta y}{0}$ = undefined (dividing by zero is undefined)

And in a horizontal line, there is no change in y. So,

$\displaystyle slope=\frac{0}{\Delta x}=0$

3. ## ok....

Originally Posted by masters
Hello magentarita,

Let's just talk about the definition of slope. It's the change in y divided by the change in x.

$\displaystyle slope=\frac{\Delta y}{\Delta x}$

In a vertical line, there is no change in x. It remains constant. Therefore,

$\displaystyle slope=\frac{\Delta y}{0}$ = undefined (dividing by zero is undefined)

And in a horizontal line, there is no change in y. So,

$\displaystyle slope=\frac{0}{\Delta x}=0$
Very simply put. Thank you very much. Merry Christmas.