Question

1. jonas has a certain number of dvds in his collection. the table shows the total number of dvds in his collection over several months. assume the relationship between the two quantities is linear. find and interpret the rate of change and the initial value. (example 1)

month, t	3	6	9	12

Explanation:

Step1: Calculate rate of change

The rate of change (slope) $m$ for a linear relationship is $\frac{y_2-y_1}{x_2-x_1}$. Using points $(3,18)$ and $(6,27)$:
$$m=\frac{27-18}{6-3}=\frac{9}{3}=3$$

Step2: Find initial value (y-intercept)

Use linear equation $y=mx+b$, substitute $m=3$, $x=3$, $y=18$:
$$18=3(3)+b$$
$$18=9+b$$
$$b=18-9=9$$

Step3: Interpret values

Rate of change = 3 means Jonas adds 3 DVDs per month. Initial value = 9 means he started with 9 DVDs.

Answer:

The rate of change is 3, which means Jonas adds 3 DVDs to his collection each month. The initial value is 9, which means Jonas started his collection with 9 DVDs.