Chapter 11: Q1B. (page 670)

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$- 2 x = y$

Short Answer

Expert verified

The equation represents a direct variation.

Step by step solution

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

The relationship of the form $y = k x, x = \frac{y}{k}, y = \frac{k}{x}$ 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.

The relationship of the form $x y = k$ is known as inverse variation. Observe that the given equation can be further simplified as:

$- 2 x = y \frac{- 2 x}{- 2} = \frac{y}{- 2} x = - \frac{y}{2}$

is not comparable with $x y = k$ i.e., the product is not constant so the equation doesn’t represent the inverse variation.

Step 3. Check for direct variation.

The relationship of the form $y = k x$ is known as direct variation. Comparing the given equation $x = - \frac{y}{2}$ & $x = \frac{y}{k}$ , observe that $k = - 2$ , therefore, the product is constant so the equation represents the direct variation.

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Determine whether each table or equation represents an inverse or a direct variation. Explain.
$- 2 x = y$

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.−2x=y

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

Statistics

Decision Maths

Logic and Functions

Probability and Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$- 2 x = y$