Chapter 3: Q18. (page 205)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = 2$ when $x = - 12$ , what is y when $x = - 4$ ?

Short Answer

Expert verified

The value of y when $x = - 4$ is $\frac{2}{3} .$

Step by step solution

Step 1. State the concept of Direct Proportionality.

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. The proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is " $\propto$ ".

Here yvaries directly as x.

That is, $y \propto x$

Therefore $y = k x \dots (1)$

Where, kis a constant.

Step 2. Find the value of ‘k’.

Find the value of k by substituting $y = 2 and x = - 12$ in equation $y = k x$

$\begin{matrix} 2 = k (- 12) \\ \frac{2}{- 12} = \frac{- 12 k}{- 12} \\ \frac{1}{- 6} = k \\ k = \frac{1}{- 6} (Equation 2) \end{matrix}$

Step 3. Calculate the value of ‘y’

Calculate the value of y by substituting $x = - 4 and y = \frac{1}{- 6}$ in $y = k x$

$y = (\frac{1}{- 6}) (- 4) y = \frac{2}{3}$

Thus, the value of y is $\frac{2}{3}$ .

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Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = 2$ when $x = - 12$ , what is y when $x = - 4$ ?

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of ‘k’.

Step 3. Calculate the value of ‘y’

One App. One Place for Learning.

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Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solveIfy=2whenx=−12, what is y whenx=−4?

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of ‘k’.

Step 3. Calculate the value of ‘y’

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = 2$ when $x = - 12$ , what is y when $x = - 4$ ?