The table shows the number of parts, , a machine

Question

produces each hour, . Write an equation for this
situation, and indicate if this is proportional or
nonproportional.
(number of parts) (number of hours)
0 0
125 1
250 2
375 3
500 4
(1 point)
y
x
y x
y = 125x + 1, nonproportional
y = 125x, proportional
y = 125x, nonproportional
y = x + 125, nonproportional

Answer 1

To analyze the given data, the number of parts produced per hour (y) and the number of hours worked (x) can be represented in a table:

• 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 data, we can see that as the number of hours (x) increases, the number of parts (y) increases in a consistent manner. Specifically, for every one hour (increase in x), the number of parts produced (y) increases by 125. This indicates a direct relationship.

To find the equation that describes this situation, we can deduce that:

\(y = 125x\).

Since this equation passes through the origin (0,0), it indicates a proportional relationship. In proportional relationships, if \(x = 0\), then \(y\) is also 0, and the ratio of \(y\) to \(x\) remains constant.

Thus, the correct equation is:

y = 125x, proportional.