The table shows the number of parts, y

Question

, a machine produces each hour, x
. Write an equation for this situation, and indicate if this is proportional or nonproportional.

y
(number of parts) x
(number of hours)
0 0
125 1
250 2
375 3
500 4
(1 point)
Responses

y=125x
, proportional
y equals 125 x , proportional

y=x+125
, nonproportional
y equals x plus 125 , nonproportional

y=125x
, nonproportional
y equals 125 x , nonproportional

y=125x+1
, nonproportional
y equals 125 x plus 1 , nonproportional
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Answer 1

To find an equation for the situation based on the given data:

1. We can observe that when \( x = 0 \), \( y = 0 \), which indicates that when no hours are worked, no parts are produced. This is a characteristic of a proportional relationship.

2. The relationship can be seen as linear. Each hour, the machine produces 125 parts. The pattern shows that for every hour increase in \( x \), \( y \) increases by 125.

From this information, we can write the equation for the number of parts produced \( y \) as a function of hours \( x \):

\[ y = 125x \]

Since the equation goes through the origin (0,0), it confirms that the relationship is proportional.

Therefore, the correct response is:

y = 125x, proportional.