How To Interpolate
Question
In the math equation if X equals 10 then Y equals
In this video, I'm going to teach you how to interpolate. Now, to interpolate, first of all, you need a graph, and to create a graph, you need the data, so I'm going to draw the graph. This is my X axis, this is my Y axis. Now, in my graph, this is going to represent the age of children, and this is going to represent their heights. So, I must label it height and age. Now, let's say I just have a scatter plot of data that looks something like this. And if you want to know how to create a scatter plot, please see my other video. So, with this scatter plot of age versus height, we need to draw the line of best fit. Now, the line of best fit looks something like this here. Now, this point here is called the Y intercept, it is where it crosses the Y axis, and it is roughly the height of a child that has just been born. In this case, I'm going to say this Y intercept is forty, so, where? Next to zero, our Y is forty. Now, you can also figure out the equation for this line using the computer or by figuring out the gradient. In this case, my gradient is ten, so the equation of my line y = 10x +40. Okay, so first of all, how to interpolate graphically. Let's say you have a child, age ten, and you want to work out what height, according to the data, that that child roughly is. The way we do that is we draw a line vertically up from ten until we hit the line of best fit right here. And then, draw along horizontally until we hit the Y axis. And that point there is 140 centimetres. Now, if we have a child, age ten, we draw up, and we draw along and this should be 140 centimetres. Alternatively, we can interpolate using the equation. And we take our x value along the X axis, which is ten, and put it into here, so we have Y equals ten times forty, which is one hundred and forty. So y = 140. So, when x is 10, y is 140, and there you've interpolated using the equation. So, you can either interpolate graphically by drawing up and along, or you can interpolate using the equation here. Now, there's one more thing you can do, let's say you have a child whose height is 180 centimetres, and you want to figure out roughly how old that child is. So, you draw along, from your 180, you draw along here, until you hit the line of best fit, exactly the same, and you come down until the X axis, and you hit 14. So, this child is 14, so roughly, a child of 14 is 180 centimetres tall. And that is how you interpolate. .