Why 2D linear interpolation formula sums the initial point's y component?

Question

$$y=y1+(x-x1)\frac{y2-y1}{x2-x1}$$ https://matthew-brett.github.io/teaching/linear_interpolation.html

I've seen this formula in multiple places and I'm wondering why do we need to multiply the distance between $x$ and $x1$ to the slope and add it to $y1$ when this formula would work just the same: $$y=x\frac{y2-y1}{x2-x1}$$

That other formula does definititely not work just the same (unless the line happens to pass through the origin). Have you tried plugging in some numbers to see what happens? — Hans Lundmark, Mar 25 '21 at 21:15
I actually tried pluging in numbers but only the ones that cross the origin. I think that answered my question. — Danilo Souza Morães, Mar 29 '21 at 17:28
If you want to make this into an answer I'll accept it. Considering the origin wasn't very intuitive to me at first. — Danilo Souza Morães, Mar 29 '21 at 18:08

score 1 · Accepted Answer · answered Mar 29 '21 at 19:27

1

The two formulas only give the same result if the line goes through the origin. The first formula is the correct one.

answered Mar 29 '21 at 19:27

Hans Lundmark

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Why 2D linear interpolation formula sums the initial point's y component?

1 Answers1