Referring to unnamed lines on number line

[Beeno]

I know this is super basic, but how do you refer to the lines in these graphs? For the first graph you can use intervals but is that the standard way or would the y position ever be used in referring to the lines? I don't think intervals can be used at all in the second graph. How do you refer to the lines in the second graph? I know how I can do it good enough to communicate the coordinates but I'm not sure of the standard notation for it.

 

[Dr.Peterson]

I'm confused. These lines are not on the number line; they are on the coordinate plane!

You can describe them by their equations, together with domains; the first can be described by a piecewise-defined function, and the second pair are parallel lines over the same domain.

It may help if you tell us the context of your question. Are you trying to solve a particular problem or answer a specific question? Then tell us exactly how the whole problem was stated.

 

[HallsofIvy]

The first graph has two parts, one a straight line from (0, 2) to (20, 4), the second a straight line from (20, 4) to (40, 2). Any straight line can be written "y= ax+ b" for some numbers, a and b, and two points give us two equations to solve for a and b.

The first line goes through (0, 2) so 2=a(0)+b and through (20, 4) so 4= a(20)+ b.
Solve the two equations, b= 2 and 20a+ b= 4.

Do the same for the line through (20, 4) and (40, 2).

When writing the formula for the entire graph be sure to say that the first equation applies for x between 0 and 20 and the second applies for x between 20 and 40.

The second graph has two parallel lines so will have two different equations for the same x values (x between 10 and 30). One line is from (10, 2) to (30, 4) so what is its equation? The other is from (10, 4) to (30, 6) so what is its equation?