Question

Why does a horizontal line have a slope of zero, but a vertical line have an undefined slope?

Answer 1

Refer to the diagram shown below.
Define two positions on each line as A (x₁, y₁) and B(x₂, y₂).
Then the slope is

`m= (y_(2)-y_(1))/(x_(2)-x_(1))`

Horizontal line:
Define A (0, 1) and B (1,1).
The slope is

`m= (1-1)/(1-0)=0`

Vertical line:
Define A( (1,0) and B(1,1).
The slope is

`m= (1-0)/(1-1)= (1)/(0)` (undefined)