Creating equation out of 5 point or more from graph plot.

In summary, the conversation discusses different methods for determining the equation of a graph line from a given set of points. These methods include drawing a polynomial curve, fitting a straight line using least squares, and considering other factors such as accuracy and known formulas. Ultimately, the level of accuracy and the purpose of the equation will determine the best approach to use.
  • #1
David Roger
2
0
Hi,

I need to find the 6th point of a graph line. The line is not totally straight.

Is there step I can take to find the equation from the 5 point alone?
 
Physics news on Phys.org
  • #2
Depends on what exactly you want.
You can always draw a fourth degree polynomial through the five points (i.e. determine a, b, c, d, e in y = ax4 + bx3 + cx2 + dx + e).
Or you can draw a straight line that doesn't go through all the points but comes as close to them as possible (e.g. do a least square fit).
Or you can just write down some ugly (non-differentiable) function going through the five points.
 
  • #3
I have Point 1 (1103, 7093.16702) and Point 2 (1104, 20553.56911).

How do I ever determine the equation correctly?
 
  • #4
Again, which equation do you want?
You can draw straight lines between each pair of points but that will give you a very "edgy" graph. You can find a smooth polynomial through the points, but that will not be of much use if you want to, say, extrapolate the data.
Or you can do a fit of a straight line (or other function) which will be of use for extrapolating, but then the given points will not necessarily be on the line.
 
  • #5
David Roger said:
I have Point 1 (1103, 7093.16702) and Point 2 (1104, 20553.56911).

How do I ever determine the equation correctly?

Well, you can determine a straight line that passes through these two points pretty easily, but unfortunately, the techniques involved in that won't really help you here, where you're trying to find a non-linear curve from 5 points. You can find a 4th order polynomial that will exactly touch all five of your points, but a lot of times (like CompuChip said) this will be useless for extrapolating, because it will tend to oscillate between the points and then shoot off into space on both ends. Unfortunately, curve fitting is not as easy as it seems like it should be.

To help you answer this, more information is needed:
-what's the project that this is for? (how important is accuracy?)
-what exactly is the problem you're solving? (is there some known formula that you would expect to describe your results?)
 
  • #6
Could try using least squares to give you an nth order polynomial but if that 6th point isn't between your first and last ones then it won't really help (not that it'd help much if it wasn't)
Also, to get the line between point 1 and 2 it's just the basic
y = m x + c
y = (delta x/delta y)x + c

don't see how much use that would be to you though
 

1. How do I create an equation from a graph plot with 5 points or more?

To create an equation from a graph plot with 5 points or more, you will need to use the slope-intercept form of a linear equation, y = mx + b. First, identify at least 2 points on the graph plot and calculate the slope (m) using the formula (y2 - y1) / (x2 - x1). Then, substitute the slope and one of the points into the equation and solve for b. Once you have the value of b, you can write the equation in the form y = mx + b with the calculated values of m and b.

2. Can I create an equation from a graph plot with a curve or non-linear shape?

Yes, you can create an equation from a graph plot with a curve or non-linear shape. However, it may be more challenging and require advanced mathematical techniques such as curve fitting or using a regression model. These methods involve finding the best fit line or curve that passes through the given points on the graph plot.

3. What if I only have 3 points on my graph plot, can I still create an equation?

It is possible to create an equation with only 3 points on a graph plot, but it may not accurately represent the entire data set. The minimum number of points needed to create a linear equation is 2, but having more points will result in a more accurate representation of the data.

4. Can I use a graphing calculator to create an equation from a graph plot?

Yes, most graphing calculators have a function to find the equation of a line or curve from a given set of points on a graph plot. However, it is important to note that some calculators may use different methods or algorithms to determine the equation, which may result in slightly different answers. It is always recommended to double-check the equation manually if possible.

5. What is the importance of creating an equation from a graph plot?

Creating an equation from a graph plot allows us to represent and make predictions about the data in a more organized and concise manner. It also allows us to better understand the relationship between the variables and make comparisons between different data sets. Equations can also be used to make future predictions and solve real-world problems in various fields such as economics, physics, and engineering.

Similar threads

  • Calculus
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
620
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
772
Replies
3
Views
820
  • Calculus
Replies
5
Views
2K
  • Precalculus Mathematics Homework Help
Replies
20
Views
1K
Replies
49
Views
1K
  • Programming and Computer Science
Replies
3
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
72
Back
Top