Recall that two quantities are if they have a constant or . For relationships in which this ratio is not constant, the two quantities are not proportional. We want to determine which situation represents a proportional relationship between the heights of the plants and number of weeks. Let's start by writing all the information about Plant A in a table.
| Height of Plant A (inches)
|
18
|
36
|
56
|
| Number of Weeks
|
1
|
2
|
3
|
We can write the relationship of the height of Plant A and the number of weeks that have passed as a ratio in simplest form.
| Height of Plant A (inches)
|
18
|
36
|
56
|
| Number of Weeks
|
1
|
2
|
3
|
| Ratio (inches per week)
|
18/1=18
|
36/2=18
|
56/3
|
As we can see, the ratios of the two quantities are not the same, which means that the relationship between the height of Plant A and the number of weeks is not proportional. Now let's consider Plant B. Let's gather all the information about Plant B in a table.
| Height of Plant B (inches)
|
18
|
36
|
54
|
| Number of Weeks
|
1
|
2
|
3
|
Like we did before, we can write the relationship of the height of Plant B and number of weeks passed as a ratio in simplest form.
| Height of Plant B (inches)
|
18
|
36
|
54
|
| Number of Weeks
|
1
|
2
|
3
|
| Ratio (inches per week)
|
18/1=18
|
36/2=18
|
54/3=18
|
As we can see, all of the ratios between the two quantities can be simplified to 18. This means that the relationship between the height of Plant B and number of weeks is proportional.
