Question

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

Answer 1

To determine the correct equation and whether the relationship is proportional or nonproportional, let's analyze the data 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 this, we can see that as \( x \) increases by 1 hour, \( y \) increases by 125 parts. This suggests a linear relationship.

To form the equation, we notice:
- The slope (rate of production) is 125 parts per hour.
- When \( x = 0 \), \( y = 0 \) which suggests that the equation starts from the origin.

This leads us to the equation:

\[
y = 125x
\]

Since this equation goes through the origin (0,0) and has a constant rate of change, it is a proportional relationship.

Thus, the correct answer is:

\[ y = 125x, \text{ proportional.} \]