Question

If a line has a slope of zero, how is it oriented?

Answer 1

We can find the slope of any line by thinking about the changes in its x-y coordinates, given by the formula:


`(y_1 - y_2)/(x_1 - x_2), \text{ } x_1 \\eq x_2`

For there to be a slope of zero, then the two y-ordinates must be the same, given the x-ordinates aren't the same.

This resembles our horizontal line, given by the equation:

`y = a,\text{ }a \in \mathbb{R}`

We know this because the changes in the y-ordinate is zero, giving us a gradient/slope of zero.

Answer 2

A line with a slope of zero is a horizontal line having the general equation of y = b.