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the time (y) that it takes a machine to produce a batch of items is directly proportional to the number of items in the batch (x).If it takes 17 minutes to produce 5 items,Which equation models this situation?

the time y that it takes a machine to produce a batch of items is directly proportional to the number of items in the batch xIf it takes 17 minutes to produce 5 class=

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kudzordzifrancis

ANSWER

A. y=3.4x

EXPLANATION

It was given that, the time (y) is directly proportional to the number of items (x).

We can write this mathematically as:

[tex]y \propto \: x[/tex]

If we introduce the constant of proportionality, we obtain;

[tex]y = kx[/tex]

If y=17 and x=5, then,

[tex]17 = 5k[/tex]

[tex]k = 3.4[/tex]

Hence the equation that models the situation is;

[tex]y = 3.4x[/tex]

luisejr77

Answer: Option A

Step-by-step explanation:

A direct proportion equation has the form:

[tex]y=kx[/tex]

Where "k" is the constant of proportionality.

Knowing that it takes 17 minutes to produce 5 items, you can find k by substituting 17 minutes and 5 items  into the equation and solving for k:

[tex]y=17\\x=5[/tex]

[tex]17=k(5)\\k=\frac{17}{5}\\\\k=3.4[/tex]

Now, susbtitute k into [tex]y=kx[/tex] to find the equation that models this situation:

[tex]y=3.4x[/tex]

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