Q&A for How to Determine Whether Two Variables Are Directly Proportional

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Does a direct proportion need to have a slope of 0?

Donagan

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No. A zero slope means there's no change at all; thus, no proportionality at all.

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How do I solve indirect proportion?

Donagan

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If you're referring to inverse proportionality, such a case can be represented by xy = k, or y = k/x, or x = k/y, where x and y are variables, and k is a constant. If you can express x and y by any of those equations, you know that x and y are inversely proportional to each other (meaning that x goes up at the same rate that y goes down, or vice versa).

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In your example of ordered pairs x = 2, 4, 6 and y = 1, 2, 3, only the first two a and y values increased by the same constant of 2, yet you said that the example was a direct variation. Why?

Donagan

Top Answerer

It is a "direct variation," because each x value is related identically to the corresponding y value (x = 2y). We call this a direct proportion.

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Does a direct proportion have to be linear?

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If by linear you mean a straight line on a graph, the answer is yes. The graph of the direct proportion "y = kx" (or y = mx + b) is always a straight line.

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What is a dependent variable?

Donagan

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It is a variable whose value "depends" on the value of another variable. An example: y = 2x² + 3x + 1. You can't find the value of y until you know the value of x, so y is the dependent variable.

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What are two ways to determine whether a relationship is proportional?

Donagan

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(1) Graph the relationship. If the graph is a straight line having a slope that is neither zero nor infinity, the relationship between the variables is proportional; (2) Inspect the equation to see if it has (or can be made to have) the form y = kx, or x = ky, where k is a constant.

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Can it be linear if it is not directly proportional?

Donagan

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If by linear you mean having a "straight slope," then no.

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