The table shows the number of parts, y, a machine produces each hour, z. Write an equation for this situation, and indicate if this is proportional or nonproportional.

Question

y (number of parts), z (number of hours)
(0,0)
(1, 125)
(2, 250)
(3, 375)
(4, 500)

y=125z, nonproportional

y=125z+1, nonproportional

y=125z, proportional

y=x+125, nonproportional

Answer 1

To analyze the data provided and determine the correct equation, let's observe the relationship between \(y\) (the number of parts produced) and \(z\) (the number of hours):

The points listed in the table are:

• (0, 0)
• (1, 125)
• (2, 250)
• (3, 375)
• (4, 500)

From these values, we can see that as \(z\) increases by 1 hour, \(y\) increases by 125 parts. This indicates a constant rate of production.

1. The relationship can be modeled by the equation: \[ y = 125z \] This equation indicates that for every hour (\(z\)), the machine produces 125 parts (\(y\)).

2. To determine if the relationship is proportional or nonproportional, we note that:

   • A proportional relationship is one in which the ratio \( \frac{y}{z} \) is constant (and \(y = k \cdot z\) with \(k\) being a non-zero constant) and passes through the origin (0,0).
   • The equation \(y=125z\) satisfies both of these conditions:
     • It passes through the origin.
     • The ratio \( \frac{y}{z} = 125\) is constant.

Thus, the correct conclusion is:

• The equation is \(y = 125z\).
• The relationship is proportional.

Therefore, the correct choice is: y = 125z, proportional.