Chapter 3: Q36. (page 203)

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 $y = - 3$ .

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 $y = - 3$ is $\frac{9}{2}$ .

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 $x = 9, y = - 6$ .

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

$\begin{matrix} y = k x \\ - 6 = k (9) \\ \frac{- 6}{9} = k \\ \frac{- 2}{3} = k \end{matrix}$

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

Therefore, it is obtained that:

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

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=−3.

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

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

$\begin{matrix} y = \frac{- 2}{3} x \\ - 3 = \frac{- 2}{3} x \\ - 9 = - 2 x \\ \frac{- 9}{- 2} = x \\ \frac{9}{2} = x \end{matrix}$

Therefore, the value of x when $y = - 3$ is $\frac{9}{2}$ .

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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 $y = - 3$ .

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=−3.

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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=−3.

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=−3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Mechanics Maths

Statistics

Geometry

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 $y = - 3$ .