A bivariate is a polynomial or function with exactly two variables.
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A bivariate equation.
When the correlation coefficient isn't equal to 1 you have any number of choices. Contrary to what a maths syllabus might tell you, there is no right or wrong answer here. Do whatever you think best! Maths does have a creative element to it (this isn't it though...) If its close to zero though, a regression line is probably a poor choice. There aren't many ways to draw a nice fitting curve in this case, but you might be able to model it with a random (e.g. bivariate normal) distribution.