Question

After 6 months, the total cost of Tanya’s gym membership was $200. After 8 months, the total cost was $260. Is this a proportional or non-proportional relationship? Question 11 options: Proportional; the constant of proportionality is $33.33/month Proportional; the constant of proportionality is $32.50/month Non-proportional; the rate of change is $20/month Non-proportional; the rate of change is $30/month

Answer 1

Answer:

Non-proportional; the rate of change is $30/month

Step-by-step explanation:

After 6 months, the total cost was $200.

After 8 months, the total cost was $260.

Find the rate of change using formula

$\dfrac{f(b)-f(a)}{b-a}$

Hence,

$\text{Rate of change}\\ \\=\dfrac{\ 260-\ 200}{8-6}\\ \\=\dfrac{\ 60}{2}\\ \\=\ 30\ \text{per month}$

At this rate, after 6 months Tanya paid

$\ 30\cdot 6=\ 180$

But after 6 months, the total cost of Tanya’s gym membership was $200.

It means the relationship passes through the point (0,20), not through the origin. Each proportional realtionship passes through the origin. Thus, this is not proportional relationship.