Question

1 point

1) 8.EE.5: The number of bottles a machine fills is proportional to the
number of minutes the machine operates. The machine fills 250 bottles
every 20 minutes. Which graph shows the number of bottles, y, the
machine fills in x minutes. *

Answer 1

`y = 250x`

Explanation:

The options are not given; however, the question can still be answered.

Given

Direct Proportion:

In 20 minutes, y = 250 bottles

Required

Determine the graph

In the first 20 minutes, y = 250

In the next 20 minutes, y = 250 + 250 = 500

In the next 20 minutes, y = 500 + 250 = 750

This gives a arithmetic sequence:

250, 500, 750, ........

Next, is to determine the equation of the sequence using;

`T_n = a + (n - 1)d`

In this case;

`T_n = y`

`x = n`

`a = 250`

`d = 750 - 500 = 500 - 250 = 250`

Substitute these values in the above formula;

`y = 250 + (x - 1) * 250`

Open Bracket

`y = 250 + 250x - 250`

Collect Like Terms

`y = 250x + 250 - 250`

`y = 250x`

Hence; the graph that shows the given description is the graph with equation
`y = 250x`