Suppose the table has two columns, one for a variable X and the other for a variable Y.
Suppose
xi is associated with yi
for i = 2, 3, etc.
If, y1 - yj = k(x1 - xj) where k is the same constant for each index j, then the equation is linear.
If the values of X are evenly spaced, the task is easy. All you need check is that the values of Y are also evenly spaced. But the Xs may not be evenly spaced.
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I'm not sure how you managed to get your equation into a table form. So perhaps try multiply each pronumeral by an exponential of the index of the third pronumeral cow
You can easily tell by substituting 0 for a.
You could put the equation in slope-intercept form or in parent linear function or even make a table of values.
If the two equations are linear transformations of one another they have the same solution.
An equation is a statement that two things are equal. A function is a rule or process that gives you a value if you give it something in its domain (the set of things on which it is defined) as an argument. Functions on numbers that are defined by a rule can usually be expressed by an equation. A linear function is one that can be defined by a linear equation.