Minutes Machine P Machine Q Machine R
2 12 18 14
6 24 54 42
12 48 108 70
Which of these represents a proportional relationship? Write an equation to represent
this relationship where y is the number of parts produced in x minutes.
The relationship between Machine P and Machine Q is proportional.
To check this, we can compare the ratios of parts produced in the same amount of time for each machine. For example, in 2 minutes Machine P produced 12 parts and Machine Q produced 18 parts. The ratio of parts produced by Machine P to Machine Q is 12:18, which simplifies to 2:3.
Similarly, in 6 minutes Machine P produced 24 parts and Machine Q produced 54 parts. The ratio of parts produced by Machine P to Machine Q is 24:54, which simplifies to 4:9.
In both cases, the ratios are the same. Therefore, the relationship between Machine P and Machine Q is proportional.
An equation to represent this relationship where y is the number of parts produced in x minutes for Machine P can be written as:
y = 6x
And for Machine Q:
y = 9x