Chapter 3: Q35. (page 203)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 15$ when $x = 2$ , find y when $x = 8$ .

Short Answer

Expert verified

The direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

The value of y when $x = 8$ is 60.

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 $y α x$ .

Therefore, it is obtained that:

$\begin{array}{l} y α x \\ y = k x \end{array}$

Where k is constant of proportionality.

It is given that when $x = 2$ , $y = 15$ .

Therefore, substitute 2 for x and 15 for y in the equation $y = k x$ to find the value of k.

$\begin{matrix} y = k x \\ 15 = k (2) \\ \frac{15}{2} = k \end{matrix}$

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

Therefore, it is obtained that:

$\begin{matrix} y = k x \\ y = \frac{15}{2} x \end{matrix}$

Therefore, the direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

Step 2. Find the value of y when x=8.

The direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

Find the value of y by substituting 8 for x in the equation $y = \frac{15}{2} x$ .

$\begin{matrix} y = \frac{15}{2} x \\ y = \frac{15}{2} (8) \\ y = 15 (4) \\ y = 60 \end{matrix}$

Therefore, the value of y when $x = 8$ is 60.

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Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 15$ when $x = 2$ , find y when $x = 8$ .

Short Answer

Step by step solution

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

Step 2. Find the value of y when x=8.

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Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.Ify=15 when x=2, find y when x=8.

Short Answer

Step by step solution

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

Step 2. Find the value of y when x=8.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Decision Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 15$ when $x = 2$ , find y when $x = 8$ .