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In an algebraic expression (or equation), a coefficient is the numerical multiplier for a term. If the coefficient is, itself, a variable, then it is a parameter.

For example, the equation of a straight line in 2-d is

y = mx + c

where

x and y are the coordinate variables,

m is the parameter which defines the slope, and

c is the parameter which defines the y-intercept.

Different values of m will give a set of lines with the same intercept, whereas different values of c will give a set of lines with the slope. Varying both, together, will generate all possible lines.

By contrast, in the equation y = 2x + 5, 2 is the coefficient of x and 5 is the constant [coefficient]. They are specific values of the parameter whic define a specific line.

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Q: What is the difference between coefficient and parameter?
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