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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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