Question Find $y$ varies directly with $x$ . If $x=5$ then $y=15$ . Determine the constant of variation $k$ .

Studdy Solution

STEP 1

Assumptions
1. $y$ varies directly as $x$ , which means $y = kx$ for some constant $k$ .
2. When $x = 5$ , then $y = 15$ .
3. We need to find the constant of variation $k$ .

STEP 2

Since $y$ varies directly as $x$ , we can write the relationship as:
$y = kx$

STEP 3

Now, plug in the given values for $x$ and $y$ to solve for $k$ .
$15 = k \cdot 5$

STEP 4

Divide both sides of the equation by 5 to isolate $k$ .
$\frac{15}{5} = k$

STEP 5

Calculate the value of $k$ .
$k = 3$
The constant of variation $k$ is 3.

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Question Find $y$ varies directly with $x$ . If $x=5$ then $y=15$ . Determine the constant of variation $k$ .

Studdy Solution

STEP 1

Assumptions
1. $y$ varies directly as $x$ , which means $y = kx$ for some constant $k$ .
2. When $x = 5$ , then $y = 15$ .
3. We need to find the constant of variation $k$ .

STEP 2

Since $y$ varies directly as $x$ , we can write the relationship as:
$y = kx$

STEP 3

Now, plug in the given values for $x$ and $y$ to solve for $k$ .
$15 = k \cdot 5$

STEP 4

Divide both sides of the equation by 5 to isolate $k$ .
$\frac{15}{5} = k$

STEP 5

Calculate the value of $k$ .
$k = 3$
The constant of variation $k$ is 3.

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Question Find yyy varies directly with xxx. If x=5x=5x=5 then y=15y=15y=15. Determine the constant of variation kkk.

Studdy Solution

STEP 1

Assumptions1. yyy varies directly as xxx, which means y=kxy = kxy=kx for some constant kkk.2. When x=5x = 5x=5, then y=15y = 15y=15.3. We need to find the constant of variation kkk.

STEP 2

Since yyy varies directly as xxx, we can write the relationship as:y=kxy = kxy=kx

STEP 3

Now, plug in the given values for xxx and yyy to solve for kkk.15=k⋅515 = k \cdot 515=k⋅5

STEP 4

Divide both sides of the equation by 5 to isolate kkk.155=k\frac{15}{5} = k515​=k

STEP 5

Calculate the value of kkk.k=3k = 3k=3The constant of variation kkk is 3.

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Question Find $y$ varies directly with $x$ . If $x=5$ then $y=15$ . Determine the constant of variation $k$ .

Assumptions
1. $y$ varies directly as $x$ , which means $y = kx$ for some constant $k$ .
2. When $x = 5$ , then $y = 15$ .
3. We need to find the constant of variation $k$ .

Since $y$ varies directly as $x$ , we can write the relationship as:
$y = kx$

Now, plug in the given values for $x$ and $y$ to solve for $k$ .
$15 = k \cdot 5$

Divide both sides of the equation by 5 to isolate $k$ .
$\frac{15}{5} = k$

Calculate the value of $k$ .
$k = 3$
The constant of variation $k$ is 3.