Question

Let Y be a function of X, given by the table of values below.
X: 1.25| 1.5, |1.75| 2.0 | 2.25| 2.50 |
Y: 6.25| 6.63|7.03| 7.46| 7.91 | 8.40 |
(a) Verify that for constant changes in X , the change in the function is proportional to the Y value, at least
at the same precision level as the given data (to two decimal places).
(b) Using this value, find an approximate formula for Y in terms of X .

By doing +A to each X to get Y, I noticed that:
The +A was
5, 5.13, 5.28, 5.46, 5.66, 5.9

So I thought the equation must be X"something" +5, thus not sure on what variable change is used.

Answer 1

I've tried finding the slope of the final X and Y values - the first X and Y values and got
y=mx+b as y=1.72*x+4.1 but it doesn't work for the other X values.

Answer 2

The slope is change in y over change in x.

Looking at the y differences, the average is roughly 0.43 so

the slope is 0.43 over 0.25 is roughly 1.72

Then use that and the average of X and Y values in Y= mX +C in order to find C (looks close to 4)

Answer 3

I tried that earlier, you'll see in my previous post that is what I got, I did 7.03=1.72x1.75+4, but when I do 1.72x1.75+4 I get 7.01 which is not the original y value of 7.03. And the question asks the same precision level, so I am confused on if this is good enough.

Answer 4

ahh but using 4.02 works for +C, thanks for the help. I must of been punching in the wrong numbers somewhere along the line.

Answer 5

Thouhg the same C value doesn't seem to work for each one, 1.72x1.25+4.02 = 6.17 when it should be 6.25. :S

Answer 6

You would not expect to get perfect accuracy with a real set of figures so any equation is just going to be a best fit with some level of accuracy.

In the example you gave, you are off by 0.02 which is only a small error especially when you are working to 2 decimal places

Answer 7

but for X as 2 it works to make y = 7.46.

Answer 8

Ahh okay, that makes sense. Cheers.

Answer 9

ur welcome