Chapter 11: Q5. (page 672)

Graph an inverse variation equation in which $y = 16$ when $x = 4$ .

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 16 for $y$ , 4 for $x$ into the equation $x y = k$ and solve for $k$ .

$x y = k 4 \times 16 = k 64 = k$

The constant of variation is $k = 64$ . So, the equation that relates $x$ and $y$ is $x y = 64$ .

Step 3. Plot the points on the graph.

Create the table of values satisfying $y = \frac{64}{x}$ . Choose values for $x$ and $y$ that have a product of 64.

$x_{1}$	$y_{1}$
2	32
4	16
$- 2$	$- 32$
$- 4$	$- 16$
8	8
$- 8$	$- 8$
10	64
$- 10$	$- 6.4$

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

The graph obtained is:

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Graph an inverse variation equation in which $y = 16$ when $x = 4$ .

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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Graph an inverse variation equation in whichy=16whenx=4.

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

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Graph an inverse variation equation in which $y = 16$ when $x = 4$ .