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

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

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

To determine the equation for the given situation, we can analyze the relationship between the number of parts produced (y) and the number of hours (x). From the data in the table:

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

We can see that the number of parts produced increases by 125 for each additional hour. This indicates a constant rate of production, which suggests a linear relationship.

The equation that represents this situation is:

\[ y = 125x \]

The fact that when \( x = 0 \), \( y = 0 \) indicates that the relationship is proportional. In proportional relationships, the output value (y) is directly proportional to the input value (x), and the graph of this relationship passes through the origin (0,0).

Therefore, the correct response is:

y = 125x, proportional.