Question

How do you know that the slope of every horizontal line is zero

Answer 1

Let:

`\begin{gathered} P1=(x1,y1) \\ P2=(x2,y2) \end{gathered}`

If the line is horizontal, then:

`y1=y2`

The slope is given by:

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ since\colon \\ y1=y2 \\ m=(y1-y1)/(x2-x1)=(0)/(x2-x1) \end{gathered}`

Zero over any quantity is always zero, so:

`m=(0)/(x2-x1)=0`