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Q: Is every linear relationship a direct variation?

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I have recently been doing all these direct variation problems but not every linear relationship is a direct variation... But every direct variation is a linear relation!

The line doesn't go through the origin

For a start, you could get seriously ripped off every time you go shopping.

Yes, it does. Every time there are variables in direct or inverse relationship, there is a constant of proportionality.

Almost every graph shows some relationship. The relationship may besimple or complicated,linear, quadratic or more complicated,one-to-one or one-to-many,exact or approximate.

Two variables, x and y are said to be in direct variation with one another if they are related by an equation of the form y = cx where c (>0) is the constant of [direct] variation. In the coordinate plane, this equation gives rise to a straight line, through the origin, and with a gradient (slope) = c. What this means that both x and y are 0 together, and that every increase (or decrease) in x results in an increase (decrease) of c times that amount in y.

There is a direct relationship between genes and chromosomes. Every chromosome contains many genes with each gene coding for a specific protein.

there is no linear equations that has no solution every problem has a solution

There is nothing that exists in every relationship. Every relationship we enter gives us new knowledge, good or bad. In every warm blooded relationship there is usually love, friendship, companionship.

An equality symbol such as =

Linear means referring to a line, so a line must be linear! Every point on any line is a solution to the equation that defines the line.

Variation exists within the genes of every population or species as the result of natural selection. The other reason is due to neutrality of mutations.

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