Line equation With two point

Question

I have a situation where I know the two points, let's say $(6, 320)$ and $(8, 450)$. How can I get the value at any point between these two points?

$($Level$,$ Discharge$)$

$(1, 100)$

$(2, 130)$

$(3, 160)$

$(4, 220)$

$(5, 270)$

$(6, 320)$

$(8, 450)$

Thanks.

Image about calculating water level at different levels. Please have a look.

Answer 1

Given your set of points, you need to create a line of best fit. This can be done by taking any two points in your set of data and creating a line of the form of $y=mx+b$. For example, using $(6, 320)$ and $(8, 450)$ as your two points, we get $m=\frac{450-320}{8-6}=\frac{130}{2}=65$. Now we have $y=65x+b$. To solve for $b$, we can use one of our two points. $320=65(6)+b\Rightarrow b=-70$. So, our equation to find the value between $6$ and $8$ is $y=65x-70$.

Using software, it is easier to find a line of best fit that can represent a line for all of your data points (for example, if you have a TI graphing calculator, you can use their linear regression mode to do this. For your set of points, a line of best fit I got from Mathematica is $y=50.3279x+27.2131$.

Answer 2

First step .- Define your point

$$\dfrac{x-11}{y-6}=\dfrac{12-11}{8-6}$$

Second step .- Calculate distance from point (11,6)

$$LT=\sqrt{(12-11)^2+(8-6)^2}$$

$$Lxy=\sqrt{(x-11)^2+(y-6)^2}$$

Third step .- Calculate the VALUE for (x,y)

$LT->(450-320)$

$Lxy->(VALUE-320)$

$$VALUE = ...$$