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The table shows the number of parts, y , 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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1 answer

To determine the relationship between the number of parts produced per hour and the hours worked, we can analyze the provided data:

  • When \( x = 0 \), \( y = 0 \)
  • When \( x = 1 \), \( y = 125 \)
  • When \( x = 2 \), \( y = 250 \)
  • When \( x = 3 \), \( y = 375 \)
  • When \( x = 4 \), \( y = 500 \)

From the data, we can see that as \( x \) increases by 1 hour, \( y \) increases by 125 parts. This shows a direct linear relationship between \( x \) and \( y \).

The equation of the line that represents this relationship can be written as: \[ y = 125x \]

Since the relationship passes through the origin (0,0), we can also conclude that this is a proportional relationship.

Thus, the correct response is:

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