Question

Why does a horizontal line have a slope (0) but a vertical line does not?

Answer 1

This might help....
http://www.mathwords.com/xyz/zero_slope.htm

Answer 2

Why does a line with points that have the same y-coordinate have a slope that equals 0, while a line with points that have the same x-coordinate has a undefined slope.

Answer 3

This is a good question. You could instead write your functions "parametrically" which just means instead of representing y as a function of x we have y and x both functions of a separate parameter, and this is commonly done in calculus and higher math.

For right now if that seems too intimidating, is you could think of x=3 being like the vertical version of the graph y=3. I'd be happy to explain what parametric functions are if you're interested though. =D

Answer 4

What are they? :)

Answer 5

You could think of a vertical line as having a slope of \(\pm \infty\).

Ultimately, the slope of a vertical line is undefined because \[
\frac{y_2-y_1}{x_2-x_1} = \frac{y_2-y_1}{0}
\]And division of a finite quantity \(y_2-y_1\) by \(0\) does not result in a finite quantity.