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There are two cases to consider. The first is one in which you have a table which is generated using a linear equation and you merely want to reproduce the linear equation.Select any two distinct points, each of which will be represented by an ordered pair.
Suppose the pairs are (p, q) and (r, s).
Then the gradient of the line is (q - s)/(p - r).
Then using the point-and-gradient form of the equation:
y - s = [(q - s)/(p - r)]*(x - r)
Then simplify and rearrange to the required form.
The second case is where the table is based on observations for two variables which are linearly related. However, due to random variations or measurement errors (or rounding), the scatter plot for the data is nearly - but not quite a straight line. You will then need to use statistical techniques to obtain the equation. The best known is the method of least squares. However, this site does not support the mathematical symbols to illustrate the procedure.
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How can you model data with a linear equation?
by figuring out the equation
Why linear equation is used?
Because it fits the data. That's an extremely vague answer, but it was an extremely vague question.
What is linear interpolation used for?
Linear interpolation is used as a method used in mathematics of constructing a curve that has the best fit to a series of points of data using linear polynomials.
What is the definition of linear equasion?
A linear equation is an equation in the format y=mx+b, with y being the y-value in a data set, x being the x-value in a data set, m being the constant rate of change(also known as slope, which can be found on a graph by using rise/run, and can be found on a table as the change in y/the change in x) and b is the y-intercept(the value of y when x is 0 aka the starting point). All linear equations appear as a straight line on a graph.
How are gaps in a sequence filled in?
What you are asking is not precisely clear, but in general missing data is filled in by a process of interpolation. eg. Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
