Final answer:
To determine if the number of students at Lakeview Middle School is proportional to the number of teachers, we examine the consistent ratio of 2 teachers for every 48 students, which simplifies to 1 teacher for every 24 students. If this ratio remains unchanged with variations in total numbers, the relationship is proportional.
Step-by-step explanation:
At Lakeview Middle School, there are 2 homeroom teachers assigned to every 48 students. To determine if the number of students is proportional to the number of teachers, we can set up a ratio or a fraction. If the ratio of teachers to students is consistent across the school, then the relationship is proportional. In this case, the ratio is 2 teachers to 48 students, which simplifies to 1 teacher to 24 students.
If the school has more students but keeps this ratio constant (for example, 4 teachers for 96 students, 6 teachers for 144 students, etc.), then we can say the number of students is proportional to the number of teachers. Proportionality is about maintaining a consistent ratio, and if this ratio does not change as the number of teachers and students increases, it is considered proportional.