Question

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?

Answer 1

Answer: Option A

Explanation:

A direct proportion equation has the form:

`y=kx`

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:

`y=17\\x=5`

`17=k(5)\\k=(17)/(5)\\\\k=3.4`

Now, susbtitute k into
`y=kx` to find the equation that models this situation:

`y=3.4x`

Answer 2

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:

`y \propto \: x`

If we introduce the constant of proportionality, we obtain;

`y = kx`

If y=17 and x=5, then,

`17 = 5k`

`k = 3.4`

Hence the equation that models the situation is;

`y = 3.4x`