Chapter 11: Q6. (page 673)

Assume that $y$ varies inversely as $x$ . Write an inverse variation equation that relates $x$ and $y$ . Then graph the equation.
$y = 2$ when $x = 5$

Short Answer

Expert verified

The graph obtained is:

Step by step solution

Step 1. State the concept of inverse 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. Write the equation that relates x and y.

Since $y$ varies inversely as $x$ an inverse variation equation is given by $x y = k$ so, substitute 2 for $y$ , 5 for $x$ into the equation $x y = k$ , and solve for $k$ .

$x y = k 2 \times 5 = k 10 = k$

The constant of variation is $k = 10$ . So, the equation that relates $x$ and $y$ is $x y = 10$ .

Step 3. Plot the points on the graph.

Create the table of values satisfying $y = \frac{10}{x}$ . Choose values for $x$ and $y$ that have a product of 10.

role="math" localid="1648111803704" $x_{1}$	$y_{1}$
$- 2$	$- 5$
$- 5$	$- 2$
0	Undefined
2	5
5	2

Plot each point and draw a smooth curve that connects these points.

The graph obtained is:

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.

Assume that $y$ varies inversely as $x$ . Write an inverse variation equation that relates $x$ and $y$ . Then graph the equation.
$y = 2$ when $x = 5$

Short Answer

Step by step solution

Step 1. State the concept of inverse variation.

Step 2. Write the equation that relates x and y.

Step 3. Plot the points on the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Calculus

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Assume that yvaries inversely as x. Write an inverse variation equation that relates xand y. Then graph the equation.y=2when x=5

Short Answer

Step by step solution

Step 1. State the concept of inverse variation.

Step 2. Write the equation that relates x and y.

Step 3. Plot the points on the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Calculus

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Assume that $y$ varies inversely as $x$ . Write an inverse variation equation that relates $x$ and $y$ . Then graph the equation.
$y = 2$ when $x = 5$