Chapter 11: Q14. (page 674)

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5 6
$y$
30 15 6 5

Short Answer

Expert verified

The table represents an inverse variation.

Step by step solution

Step 1. State the concept of direct variation and inverse variation.

The relationship of the form $y = k x$ is called direct variation.

Relationship of the form $x y = k$ or $y = \frac{k}{x}$ where $x, y \neq 0$ for some nonzero constant $k$ is known as inverse variation i.e., $y$ varies inversely as $x$ .

Step 2. Check for inverse variation.

Find $x y$ each ordered pair from the table and get,

$\begin{matrix} 1 \cdot 30 = 30 \\ 2 \cdot 15 = 30 \\ 5 \cdot 6 = 30 \\ 6 \cdot 5 = 30 \end{matrix}$

The product is constant so the table represents an inverse variation, $x y = 30$ .

Step 3. Check for direct variation.

Find $\frac{y}{x}$ each ordered pair from the table and get,

role="math" localid="1648108929404" $\begin{matrix} \frac{30}{1} = 30 \\ \frac{15}{2} = 7.5 \\ \frac{6}{5} = 1.2 \end{matrix}$

\begin{matrix} \frac{5}{6} = 0.833 \end{matrix}

Since $\frac{y}{x}$ is not constant so the table doesn’t represent the direct variation.

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Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5 6
$y$
30 15 6 5

Short Answer

Step by step solution

Step 1. State the concept of direct variation and inverse variation.

Step 2. Check for inverse variation.

Step 3. Check for direct variation.

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Determine whether each table or equation represents an inverse or a direct variation. Explain.x1256y301565

Short Answer

Step by step solution

Step 1. State the concept of direct variation and inverse variation.

Step 2. Check for inverse variation.

Step 3. Check for direct variation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Mechanics Maths

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Calculus

Study anywhere. Anytime. Across all devices.

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5 6
$y$
30 15 6 5