Q15. Suppose y聽varies directly as x.... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 3: Q15. (page 205)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 6$ when $x = 9$ , find x when $y = 12$ .

Short Answer

Expert verified

The direct variation equation that relates x and y is $y = \frac{2}{3} x$ and the value of x when $y = 12$ is 18.

Step by step solution

Step 1. Write a direct variation equation that relates x and y.

It is given that y varies directly as x.

Therefore it implies that $y 伪 x$ .

Therefore, it is obtained that:

$y 伪 x y = k x$

Where is k constant of proportionality.

It is given that when $x = 9, y = 6$ .

Therefore, substitute 9 for x and 6 for y in the equation $y = k x$ to find the value of k.

$y = k x 6 = k (9) \frac{6}{9} = k \frac{2}{3} = k$

Substitute the value of k in the equation $y = k x$ .

Therefore, it is obtained that:

$\begin{matrix} y = k x \\ y = \frac{2}{3} x \end{matrix}$

Therefore, the direct variation equation that relates x and y is $y = \frac{2}{3} x$ .

Step 2. Find the value of x when y=12.

The direct variation equation that relates x and y is $y = \frac{2}{3} x$ .

Find the value of x by substituting 12 for y in the equation $y = \frac{2}{3} x$ .

$y = \frac{2}{3} x 12 = \frac{2}{3} x 12 脳 3 = 2 x 36 = 2 x \frac{36}{2} = x 18 = x$

Therefore, the value of x when $y = 12$ is 18.

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91影视

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 6$ when $x = 9$ , find x when $y = 12$ .

Short Answer

Step by step solution

Step 1. Write a direct variation equation that relates x and y.

Step 2. Find the value of x when y=12.

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.Ify=6 when x=9, find x when y=12.

Short Answer

Step by step solution

Step 1. Write a direct variation equation that relates x and y.

Step 2. Find the value of x when y=12.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 6$ when $x = 9$ , find x when $y = 12$ .