Jodie made a New Year's resolution to learn how to play the violin. She bought an Introduction to Violin class pack from the Noble Notes music shop, which covers the cost of
12 violin lessons. She also paid $25 to rent a violin. In all, Jodie paid $385. How much does
each violin lesson cost?

Part 1) Option A. Yes; y=1.5x

Part 2) Option D. No there is no direct variation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 1) we have the points

(10,15),(16,24),(20,30)

Find the value of the constant of proportionality k

For x=10, y=15

substitute

For x=16, y=24

substitute

For x=20, y=30

substitute

The value of the constant k is the same for the three ordered pairs

The linear equation is

therefore

y vary directly with x

Part 2) we have the points

(32,24),(16,8),(8,6)

Find the value of the constant of proportionality k

For x=32, y=24

substitute

For x=16, y=8

substitute

For x=8, y=6

substitute

The value of the constant k is not the same for the three ordered pairs

therefore

y not vary directly with x