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Determine the contrapositive of the statement: "If two variables are directly proportional, then their graph is a linear function."

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Final answer:

The contrapositive of the statement "If two variables are directly proportional, then their graph is a linear function" is "If a graph is not a linear function, then the two variables are not directly proportional."

Step-by-step explanation:

To determine the contrapositive of the given statement, we must first understand what the original statement and its contrapositive mean. The original statement is: "If two variables are directly proportional, then their graph is a linear function." A contrapositive of a conditional statement flips and negates both the hypothesis and the conclusion. Thus, the contrapositive would be: "If a graph is not a linear function, then the two variables are not directly proportional."

When we discuss direct proportionality, we're referring to a relationship where an increase in one variable leads to a proportional increase in the other, often represented as y = kx, where k is the constant of proportionality. In contrast, a graph that is not a straight line suggests the relationship between the variables is not of this kind.

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