QuestionFind the equation that relates $w$ and $z$ given the pairs: (18, 2), (45, 5), (81, 9).

Studdy Solution

STEP 1

Assumptions1. The relationship between $w$ and $z$ is proportional, which means $w$ is directly proportional to $z$ . . We can write the relationship as $w = kz$ , where $k$ is the constant of proportionality.

STEP 2

To find the constant of proportionality $k$ , we can use the given values of $w$ and $z$ from the table.
$k = \frac{w}{z}$

STEP 3

Now, plug in the given values for $w$ and $z$ from the first row of the table to calculate $k$ .
$k = \frac{18}{2}$

STEP 4

Calculate the value of $k$ .
$k = \frac{18}{2} =9$

STEP 5

Now that we have the constant of proportionality, we can write the equation that describes the relationship between $w$ and $z$ .
$w = kz$

STEP 6

Substitute the value of $k$ into the equation.
$w =9z$ So, the equation that describes the relationship between $w$ and $z$ is $w =9z$ .

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QuestionFind the equation that relates $w$ and $z$ given the pairs: (18, 2), (45, 5), (81, 9).

Studdy Solution

STEP 1

Assumptions1. The relationship between $w$ and $z$ is proportional, which means $w$ is directly proportional to $z$ . . We can write the relationship as $w = kz$ , where $k$ is the constant of proportionality.

STEP 2

To find the constant of proportionality $k$ , we can use the given values of $w$ and $z$ from the table.
$k = \frac{w}{z}$

STEP 3

Now, plug in the given values for $w$ and $z$ from the first row of the table to calculate $k$ .
$k = \frac{18}{2}$

STEP 4

Calculate the value of $k$ .
$k = \frac{18}{2} =9$

STEP 5

Now that we have the constant of proportionality, we can write the equation that describes the relationship between $w$ and $z$ .
$w = kz$

STEP 6

Substitute the value of $k$ into the equation.
$w =9z$ So, the equation that describes the relationship between $w$ and $z$ is $w =9z$ .

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QuestionFind the equation that relates www and zzz given the pairs: (18, 2), (45, 5), (81, 9).

Studdy Solution

STEP 1

Assumptions1. The relationship between www and zzz is proportional, which means www is directly proportional to zzz. . We can write the relationship as w=kzw = kzw=kz, where kkk is the constant of proportionality.

STEP 2

To find the constant of proportionality kkk, we can use the given values of www and zzz from the table.k=wzk = \frac{w}{z}k=zw​

STEP 3

Now, plug in the given values for www and zzz from the first row of the table to calculate kkk.k=182k = \frac{18}{2}k=218​

STEP 4

Calculate the value of kkk.k=182=9k = \frac{18}{2} =9k=218​=9

STEP 5

Now that we have the constant of proportionality, we can write the equation that describes the relationship between www and zzz.w=kzw = kzw=kz

STEP 6

Substitute the value of kkk into the equation.w=9zw =9zw=9zSo, the equation that describes the relationship between www and zzz is w=9zw =9zw=9z.

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QuestionFind the equation that relates $w$ and $z$ given the pairs: (18, 2), (45, 5), (81, 9).

Assumptions1. The relationship between $w$ and $z$ is proportional, which means $w$ is directly proportional to $z$ . . We can write the relationship as $w = kz$ , where $k$ is the constant of proportionality.

To find the constant of proportionality $k$ , we can use the given values of $w$ and $z$ from the table.
$k = \frac{w}{z}$

Now, plug in the given values for $w$ and $z$ from the first row of the table to calculate $k$ .
$k = \frac{18}{2}$

Calculate the value of $k$ .
$k = \frac{18}{2} =9$

Now that we have the constant of proportionality, we can write the equation that describes the relationship between $w$ and $z$ .
$w = kz$

Substitute the value of $k$ into the equation.
$w =9z$ So, the equation that describes the relationship between $w$ and $z$ is $w =9z$ .