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
, nonproportional
y equals 125 x , nonproportional

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

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

y=125x
, proportional

Answer 1

The relationship between the number of parts produced (y) and the number of hours (x) can be determined based on the data provided.

The pattern shows that for every hour (x), the machine produces a constant number of parts (y) that increases by 125 parts. This indicates a linear relationship. Specifically:

• At 0 hours, 0 parts are produced.
• At 1 hour, 125 parts are produced.
• At 2 hours, 250 parts are produced.
• At 3 hours, 375 parts are produced.
• At 4 hours, 500 parts are produced.

The equation that describes this situation is:

\[ y = 125x \]

Since the line passes through the origin (0,0), this situation is proportional. In proportional relationships, the ratio of y to x is constant, which in this case is 125 (as 125 parts are produced per hour).

Therefore, the correct response is:

y = 125x, proportional.