Question

Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations. $$ \begin{array}{|c|c|c|c|c|}\hline x & {0.1} & {3} & {6} & {24} \\ \hline y & {3} & {0.1} & {0.05} & {0.0125} \\ \hline\end{array} $$

Name: Problem 10, Chapter 9: Algebra 2
Uploaded: 2019-08-26T04:34:26-08:00
Duration: 2 min 32 s
Channel: Daniel Pezzi
Description: Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations. x 0.1 3 6 24 y 3 0.1 0.05 0.0125

   Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations.
$$
\begin{array}{|c|c|c|c|c|}\hline x & {0.1} & {3} & {6} & {24} \\ \hline y & {3} & {0.1} & {0.05} & {0.0125} \\ \hline\end{array}
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 9, Problem 10

Instant Answer

Solved by Expert Daniel Pezzi

08/26/2019

Step 1

Direct variation is a linear relationship where if the value of one variable increases, the other also increases. It is represented by the equation $y=kx$. Inverse variation is a relationship where if the value of one variable increases, the other decreases. It Show more…

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Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations. $$ \begin{array}{|c|c|c|c|c|}\hline x & {0.1} & {3} & {6} & {24} \\ \hline y & {3} & {0.1} & {0.05} & {0.0125} \\ \hline\end{array} $$

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Key Concepts

Direct Variation

A direct variation occurs when two variables change in the same ratio, which means one variable is a constant multiple of the other. In algebra, this relationship is typically written as y = kx, where k is the constant of proportionality. This implies that as one variable increases, the other increases proportionally.

Inverse Variation

An inverse variation occurs when one variable is a constant multiple of the reciprocal of the other. The typical model for this relationship is y = k/x, where k is the constant of proportionality. Here, as one variable increases, the other decreases in such a way that their product always equals k.

Constant of Proportionality

The constant of proportionality is a fixed constant that relates two variables in both direct and inverse variation. It quantifies how much one variable changes in response to a change in the other, and it is determined by the specific values or relationships given in a problem.

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