Explained: Linear Interpolation [Math]

In this video, I explain how to obtain the equation for linear interpolation between two points. I then go through a simple example.

Linear interpolation can be useful when you need data at points where data does not exist. This happens a lot when looking at tabulated data. Here are some examples of tabulated data where linear interpolation can come in handy:
- Steam/vapor tables in thermodynamics
- Property tables in heat transfer
- Normal shock tables and isentropic relations tables in gas dynamics

In the video linked to below, I show you how to program this equation into a graphing calculator (TI-83), so you can use it on exams or whenever you need a quick estimate.

[ercm]

Great video!!! I am here because I am learning how to control animations through scripts in Virtual Reality and Linear Interpolations is one of the most important factors that makes it happen! Just wanted to learn it a little deeper! Thanks for sharing!

[clauderobotham]

Circumstances required me to revisit interpolation for the first time in decades (since high school). Your explanation was very cogent and I think I actually understand it better now than I did then. Thanks, Josh.

[britishbuffalo]

THANK YOU FOR EXPLAINING THIS SO THOROUGHLY AND SUCCINCTLY
YOU DESCRIBED LITERALLY EXACTLY WHAT I NEEDED TO LEARN

[ezenweregozie]

Thanks so much for have been wasting my time searching for the derivation. I wish all teachers should be like you. So direct and straightforward.

[makrooneey]

Great explanation... Having an exam later today... & this helped

[Roost]

Thanks so much for showing the graphical method of linear interpolation. I am used to doing it algebraically. Very good instructive video!

[PhoenixA]

Nice, simple, clean and straight to the point, thank you very much!

[Infiniband]

Thank you for this great, simple, and easy-to-understand explanation.

[natashadavis]

This was so simple the way you explained it, thank you for your organized explanation!

[meraklmuskulpesent]

Thank you so much! Your way of teaching things is plain and effective.

[drfoxy]

I wish that I have a teacher like you for chemistry ! :D

[matone]

love the fact that he uses as an example the exact thing i want to use it on XD . (thermodynamics)

[isaissb]

Around 3:19 you say something like "we'll be able to get to the new.. Y location". This conclusion sounds a little lackluster, but overall good explanation. Multiplying the slope by the change in x will give you the change in y, which is then added to y1 to get to the new Y location.

[stashatstake]

Thank you
I needed to understand this to use a built-in function in a game engine that I am using.

[ginarapp]

Thanks so much for the video ! Really helpful for my CFA study

[MrSazid]

Dude you are good. I really appreciate how u explained to get y value just multiply the slope with x distance add it to y. I have hard time to interpret equations in plain english. thank you very much.

[Mulkek]

Thanks, and it's so easy & simple!

[maggysantana]

Joe. Thanks to show how is the formular is applicable to the problem, but you forgot to show step by step how to calculate those values so it can give you those results you plug in. That is the matris of the problem where the knowledge is getting strengths, soo please keep in mind that... let see if you have someone who doesn't never done interpolation before... he/she will be lost... so keep that in mind in your next video. Thanks

[s.r.coachingclasses.]

Respect you sir, I was finding this type of questions, thank you very much sir.

[seanmcclanahan]

My brother directed me to this cuz I was confused. Now I'm not 😀 you taught this beautifully and I'll check your channel if I am confused in the future :) Subscribed