Math / Algebra

QuestionListen
Solve for the requested variable. y varies directly as x , and $\mathrm{y}=6$ when $\mathrm{x}=3$ . Find y when $\mathrm{x}=9$ . $\square$ A

Studdy Solution

STEP 1

1. The relationship between $y$ and $x$ is a direct variation.
2. When $x = 3$ , $y = 6$ .
3. We need to find the value of $y$ when $x = 9$ .

STEP 2

1. Understand the concept of direct variation.
2. Write the equation for direct variation.
3. Find the constant of variation.
4. Use the constant to find the new value of $y$ .

STEP 3

Understand the concept of direct variation.
In direct variation, $y$ varies directly as $x$ means that $y = kx$ , where $k$ is the constant of variation.

STEP 4

Write the equation for direct variation.
Given that $y = 6$ when $x = 3$ , we can write:
$y = kx$
Substitute the known values:
$6 = k \times 3$

STEP 5

Find the constant of variation.
Solve for $k$ by dividing both sides by 3:
$k = \frac{6}{3}$ $k = 2$

STEP 6

Use the constant to find the new value of $y$ .
Now that we know $k = 2$ , substitute $x = 9$ into the direct variation equation:
$y = kx$ $y = 2 \times 9$ $y = 18$
The value of $y$ when $x = 9$ is:
$\boxed{18}$

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QuestionListen
Solve for the requested variable. y varies directly as x , and $\mathrm{y}=6$ when $\mathrm{x}=3$ . Find y when $\mathrm{x}=9$ . $\square$ A

Studdy Solution

STEP 1

1. The relationship between $y$ and $x$ is a direct variation.
2. When $x = 3$ , $y = 6$ .
3. We need to find the value of $y$ when $x = 9$ .

STEP 2

1. Understand the concept of direct variation.
2. Write the equation for direct variation.
3. Find the constant of variation.
4. Use the constant to find the new value of $y$ .

STEP 3

Understand the concept of direct variation.
In direct variation, $y$ varies directly as $x$ means that $y = kx$ , where $k$ is the constant of variation.

STEP 4

Write the equation for direct variation.
Given that $y = 6$ when $x = 3$ , we can write:
$y = kx$
Substitute the known values:
$6 = k \times 3$

STEP 5

Find the constant of variation.
Solve for $k$ by dividing both sides by 3:
$k = \frac{6}{3}$ $k = 2$

STEP 6

Use the constant to find the new value of $y$ .
Now that we know $k = 2$ , substitute $x = 9$ into the direct variation equation:
$y = kx$ $y = 2 \times 9$ $y = 18$
The value of $y$ when $x = 9$ is:
$\boxed{18}$

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QuestionListenSolve for the requested variable. y varies directly as x , and y=6\mathrm{y}=6y=6 when x=3\mathrm{x}=3x=3. Find y when x=9\mathrm{x}=9x=9. □\square□ A

Studdy Solution

STEP 1

1. The relationship between y y y and x x x is a direct variation.2. When x=3 x = 3 x=3, y=6 y = 6 y=6.3. We need to find the value of y y y when x=9 x = 9 x=9.

STEP 2

1. Understand the concept of direct variation.2. Write the equation for direct variation.3. Find the constant of variation.4. Use the constant to find the new value of y y y.

STEP 3

Understand the concept of direct variation.In direct variation, y y y varies directly as x x x means that y=kx y = kx y=kx, where k k k is the constant of variation.

STEP 4

Write the equation for direct variation.Given that y=6 y = 6 y=6 when x=3 x = 3 x=3, we can write:y=kx y = kx y=kxSubstitute the known values:6=k×3 6 = k \times 3 6=k×3

STEP 5

Find the constant of variation.Solve for k k k by dividing both sides by 3:k=63 k = \frac{6}{3} k=36​ k=2 k = 2 k=2

STEP 6

Use the constant to find the new value of y y y.Now that we know k=2 k = 2 k=2, substitute x=9 x = 9 x=9 into the direct variation equation:y=kx y = kx y=kx y=2×9 y = 2 \times 9 y=2×9 y=18 y = 18 y=18The value of y y y when x=9 x = 9 x=9 is:18 \boxed{18} 18​

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QuestionListen
Solve for the requested variable. y varies directly as x , and $\mathrm{y}=6$ when $\mathrm{x}=3$ . Find y when $\mathrm{x}=9$ . $\square$ A

1. The relationship between $y$ and $x$ is a direct variation.
2. When $x = 3$ , $y = 6$ .
3. We need to find the value of $y$ when $x = 9$ .

1. Understand the concept of direct variation.
2. Write the equation for direct variation.
3. Find the constant of variation.
4. Use the constant to find the new value of $y$ .

Understand the concept of direct variation.
In direct variation, $y$ varies directly as $x$ means that $y = kx$ , where $k$ is the constant of variation.

Write the equation for direct variation.
Given that $y = 6$ when $x = 3$ , we can write:
$y = kx$
Substitute the known values:
$6 = k \times 3$

Find the constant of variation.
Solve for $k$ by dividing both sides by 3:
$k = \frac{6}{3}$ $k = 2$

Use the constant to find the new value of $y$ .
Now that we know $k = 2$ , substitute $x = 9$ into the direct variation equation:
$y = kx$ $y = 2 \times 9$ $y = 18$
The value of $y$ when $x = 9$ is:
$\boxed{18}$