Why does dividing the final(chosen) height in a line by 2 give you the average height(y) in that line?

Question

I was taught, of course, that the average of something is the sum of all the parts divided by the number of those parts.

This is easy when it is a set of values(2, 6, 8) because its simply (2+6+8)/3 = 16/3 ≈ 5.33.

But when you have a line, you have an **infinite amount of values** divided by **infinity**, right?

So how is it even possible to take the average? And why can you simply divide it by 2 when its a line?

And then of course there is the question about the average of curves and whatnot…

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I feel so dumb, plz help me understand.

**Also this question comes from the idea that average velocity is half the final velocity**

In: 0

Answer 1

In general, just think of the graph of a linear function. No matter the slope, half of the graph is gonna be above the average value and half is gonna be below. That makes the “average” value the mean of the starting and ending points