Q18. Suppose y聽varies directly as x.... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

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 $x = 鈭� 12$ , what is y when $x = 鈭� 4$ ?

Short Answer

Expert verified

The value of y when $x = 鈭� 4$ 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 " $鈭�$ ".

Here yvaries directly as x.

That is, $y 鈥� 鈭� 鈥� x$

Therefore $y = k x 鈥夆赌夆赌夆赌夆赌夆赌� 鈥� (1)$

Where, kis a constant.

Step 2. Find the value of ‘k’.

Find the value of k by substituting $y = 2 鈥夆赌塧苍诲鈥夆赌� x = 鈭� 12 鈥夆赌�$ in equation $y = k x$

$\begin{matrix} 2 = k (鈭� 12) \\ \frac{2}{鈭� 12} = \frac{鈭� 12 k}{鈭� 12} \\ \frac{鈥夆赌� 1}{鈥� 鈭� 6} = k \\ k = \frac{鈥夆赌� 1}{鈥� 鈭� 6} 鈥夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆€夆赌夆€� (Equation鈥夆赌� 2) \end{matrix}$

Step 3. Calculate the value of ‘y’

Calculate the value of y by substituting $x = 鈭� 4 鈥夆赌塧苍诲鈥夆赌� y = \frac{1}{鈭� 6} 鈥�$ in $y = k x$

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

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

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x	y
1	$- 3$
0	$- 3$
4	$- 3$
12	$- 3$

91影视

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

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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91影视

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

Mechanics Maths

Statistics

Logic and Functions

Calculus

Probability and Statistics

Applied 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 $y = 2$ when $x = 鈭� 12$ , what is y when $x = 鈭� 4$ ?