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+1, nonproportional

y=125x, proportional

y=125x, nonproportional

y=x+125, nonproportional

Answer 1

To determine the equation that represents the relationship between the number of parts produced \(y\) and the number of hours \(x\), we can observe the values provided:

• 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 these values, we notice that for each additional hour, the number of parts produced increases by 125. Therefore, the relationship can be expressed as:

\[ y = 125x \]

Since this equation passes through the origin (0,0), it indicates a proportional relationship between the number of hours and parts produced.

Based on this, the correct response is:

y = 125x, proportional