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.
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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.
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.
This is called an "inverse" relationship.
line graph
The trend line for a scatter plot is a line that best captures the nature of the relationship between two variables. It may or may not be straight. The trend line for a scatter plot is a line that best captures the nature of the relationship between two variables. It may or may not be straight. The trend line for a scatter plot is a line that best captures the nature of the relationship between two variables. It may or may not be straight. The trend line for a scatter plot is a line that best captures the nature of the relationship between two variables. It may or may not be straight.