John paints 2 portraits in 8 hours, 3 portraits in 12 hours, and 5 portraits in 20 hours. Which statement correctly describes this situation?

Question

John paints 2 portraits in 8 hours, 3 portraits in 12 hours, and 5 portraits in 20 hours. Which statement correctly describes this situation?
A.
The given situation represents a proportional relationship because the graph of the given data does not form a straight line through the origin.
B.
The given situation does not represent a proportional relationship because the graph of the given data forms a straight line through the origin.
C.
The given situation does not represent a proportional relationship because the graph of the given data does not form a straight line through the origin.
D.
The given situation represents a proportional relationship because the graph of the given data forms a straight line through the origin.

Answer 1

The correct answer is D

 

The number of portraits is directly proportional

to the number of hours worked.

 

portraits per hour:

2/8 = 1/4, 3/12 = 1/4, 5/20 = 1/4

 

He paints 1/4 portraits per hour

 

If p is number of portraits and h is hours worked

the equation is:

 

p = (1/4)h

 

This graphs as a straight line with the start at (0, 0)