A. Let k be a nonzero constant. If y varies directly as x,...

a. Let $k$ be a nonzero constant. If $y$ varies directly as $x,$ then $y=$ ____,where $k$ is the constant of variation. b. Let $k$ be a nonzero constant. If $y$ varies inversely as $x,$ then $y=$ ____,where $k$ is the constant of variation. c. Let $k$ be a nonzero constant. If $y$ varies jointly as $x$ and $w,$ then $y=$ ____, where $k$ is the constant of variation.

a. Let $k$ be a nonzero constant. If $y$ varies directly as $x,$ then $y=$ ____,where $k$ is the constant of variation.
b. Let $k$ be a nonzero constant. If $y$ varies inversely as $x,$ then $y=$ ____,where $k$ is the constant of variation.
c. Let $k$ be a nonzero constant. If $y$ varies jointly as $x$ and $w,$ then $y=$ ____, where $k$ is the constant of variation.

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Key Concepts

Direct Variation

Direct variation describes a relationship between two variables in which one variable is a constant multiple of the other. This means that as one variable increases or decreases, the other does so proportionally. The constant of proportionality, often represented as k, is the factor by which the independent variable is multiplied to obtain the dependent variable. The typical equation for direct variation is y = kx.

Inverse Variation

Inverse variation describes a relationship where one variable is equal to a constant divided by another variable. In such a relationship, when one variable increases, the other decreases in such a way that their product remains constant. The constant of variation, denoted by k, is the product of the two variables. The standard form for an inverse variation is y = k/x.

Joint Variation

Joint variation occurs when a variable depends on two or more other variables, and it varies directly as the product of those variables. In this case, the dependent variable increases or decreases proportionally to each of the independent variables' increases or decreases, with k being the constant of proportionality. The general form of a joint variation equation is y = kxz when two variables are involved.

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