Chapter 11: Q1A. (page 670)

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5
$y$
10 5 2

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,

$1 \cdot 10 = 10 2 \cdot 5 = 10 5 \cdot 2 = 10$

The product is constant so the table represents an inverse variation, $x y = 10$ .

Step 3. Check for direct variation.

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

$\frac{10}{1} = 10 \frac{5}{2} = 2.5 \frac{2}{5} = 0.4$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5
$y$
10 5 2

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

Applied Mathematics

Geometry

Calculus

Discrete Mathematics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine whether each table or equation represents an inverse or a direct variation. Explain.x125y1052

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

Applied Mathematics

Geometry

Calculus

Discrete Mathematics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine whether each table or equation represents an inverse or a direct variation. Explain.
$x$
1 2 5
$y$
10 5 2