By definition, if you graph the relationship between two variables and the result is a straight line (of whatever slope) that is a linear relationship. If it is a curve, rather than a straight line, then it is not linear.
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The slope of a line is the same thing as the rate of change between two variables in a linear relationship.
The Correlation Coefficient computed from the sample data measures the strength and direction of a linear relationship between two variables. The symbol for the sample correlation coefficient is r. The symbol for the population correlation is p (Greek letter rho).
It means that a certain set of points are all on the same line.
Correlation between two variables implies a linear relationship between them. The existence of correlation implies no causal relationship: the two could be causally related to a third variable. For example, my age is correlated with the number of TV sets in the UK but obviously there is no causal link between them - they are both linked to time.
Linear programming is a technique for determining the optimum combination of resources to obtain a desired goal. It is based upon the assumption that there is a linear ,or straight line, relationship between variables and that the limits of the variations can be easily determined.