True or false: Given a nonvertical line, the slopes between any two of its points will be equal.
We know this is not a vertical line. Here’s an example of a nonvertical line. Here’s another nonvertical line. This one is a horizontal line. But it’s technically also a nonvertical line. Our statement is saying with the slope from point 𝑎 to 𝑏 be the same as from point 𝑏 to 𝑐.
Here’s another example on a horizontal line with the slope from 𝑎 to 𝑏 be the same as the slope from 𝑏 to 𝑐. Well, on horizontal lines, the slope is zero at both places. All three of these lines have a defined slope. And that means the slope can be determined by any two of the distinct points. That means any two of its points if you compare its slope will be equal.
And that means the statement, “Given a nonvertical line, the slopes between any two of its points will be equal is a true statement.”