In order to prove that every horizontal line has a slope of 0, let's draw the horizontal line y = 2:
Let's calculate the function that represents this line using the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Using the points (0, 2) and (1, 2), we have:
[tex]\begin{gathered} y=mx+b \\ (0,2)\colon \\ 2=0\cdot m+b \\ b=2 \\ (1,2)\colon \\ 2=m+b \\ 2=m+2 \\ m=0 \end{gathered}[/tex]
So we can see that the equation is y = 2 and the slope is m = 0.
Every horizontal line has a equation like y = b. So, comparing with the slope-intercept form, we can see that the value of m is always 0.
