y (number of parts) x (number of hours)

Question

(0)(0)
(125)(1)
(250)(2)
(375)(3)
(500)(4)
The table above 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.

Answer 1

To write an equation for the relationship between the number of parts produced (y) and the number of hours (x), we can observe the table's data points.

From the provided data:

• 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 for every additional hour (increase in \( x \)), the number of parts produced (increase in \( y \)) increases by 125 parts. This suggests a linear relationship where \( y \) increases by 125 for each increase of 1 hour.

We can find the equation of the line in the form \( y = mx + b \):

• The slope \( m \) is 125 (the rate of change of parts per hour).
• The y-intercept \( b \) is 0, since when \( x = 0 \), \( y = 0 \).

Thus, the equation can be written as:

\[ y = 125x \]

Proportional or Nonproportional

This equation represents a proportional relationship because:

1. The graph of the equation will pass through the origin (0, 0).
2. The ratio \( \frac{y}{x} \) is constant and equals 125 whenever \( x \) is not zero (or \( y \) is non-zero).

In conclusion, the equation is \( y = 125x \), and it is a proportional relationship.