Chapter 11: Q5. (page 673)

Assume that $y$ varies inversely as $x$ . Write an inverse variation equation that relates $x$ and $y$ . Then graph the equation.
$y = 8$ when $x = 6$

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 $x$ and inverse variation equation is given by $x y = k$ so, substitute 8 for $y$ , 6 for $x$ into the equation $x y = k$ , and solve for $k$ .

$x y = k 6 \times 8 = k 48 = k$

The constant of variation is $k = 48$ . So, the equation that relates $x$ and $y$ is $x y = 48$ .

Step 3. Plot the points on the graph.

Create the table of values satisfying $y = \frac{48}{x}$ . Choose values for $x$ and $y$ that have a product of 48.

$x_{1}$	$y_{1}$
$- 8$	$- 6$
$- 6$	$- 8$
$- 2$	$- 24$
0	Undefined
2	24
6	8
8	6
12	4

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

The graph obtained is:

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Assume that $y$ varies inversely as $x$ . Write an inverse variation equation that relates $x$ and $y$ . Then graph the equation.
$y = 8$ when $x = 6$

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.

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Assume that yvaries inversely as x. Write an inverse variation equation that relates xand y. Then graph the equation.y=8whenx=6

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

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Decision Maths

Statistics

Geometry

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.
$y = 8$ when $x = 6$