Chapter 3: Q17. (page 205)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = - 5$ when $x = - 2$ , what is y when $x = 14$ ?

Short Answer

Expert verified

The value of y when $x = 14$ is 35.

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 $y = k x$ … (1)

where kis a constant.

Step 2. Find the value of Constant ‘k’.

Find the value of k by substituting $y = - 5 and x = - 2$ in equation $y = k x$ .

$\begin{matrix} - 5 = k . (- 2) \\ \frac{- 5}{- 2} = \frac{- 2 k}{- 2} \\ \frac{5}{2} = k \\ k = \frac{5}{2} \end{matrix}$

Step 3. Calculate the value of ‘y’.

Calculate the value of y by substituting $x = 14 and y = \frac{5}{2}$ in $y = k x$ .

$\begin{matrix} y = \frac{5}{2} \times 14 \\ y = \frac{70}{2} \\ y = 35 \end{matrix}$

Thus the value of yis 35.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = - 5$ when $x = - 2$ , what is y when $x = 14$ ?

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of Constant ‘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

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solveIf y=−5when x=−2, what is y whenx=14?

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of Constant ‘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

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve
If $y = - 5$ when $x = - 2$ , what is y when $x = 14$ ?