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

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;

$y = 3.4x$

Answer 2

Answer: Option A

Step-by-step 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:

$y=17\\x=5$

$17=k(5)\\k=\frac{17}{5}\\\\k=3.4$

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

$y=3.4x$