Does this graph show a proportional relationship? Why or why not? Coordinate plane with x-axis labeled number of Emails and y-axis labeled Time in hours. Graph of a line contains the following points: (0, 4), (1, 5), (2, 6), (3, 7), (4, 8) and (5, 9)

Answer: No. The points given do not show a proportional relationship.

Justification:

A proportional relationship between two variables x and y means that the proportion between them is a constant. This is y = k x, or what is the same y / x = k.

Such kind of equation, y = k x, requires the the image of 0 be 0, the graph has to pass through the origin (0,0). Given the graph contains the point (0,4) you can tell inmediately that it is not a proportional relationship.

You can verify that with the other points given.

point           y/x         

(1,5)            5/1 = 5

(2,6)            6/2 = 3

(3,7)            7/3 = 2.33

(4,8)             8/4 = 2

(5,9)              9/5 = 1.8.

So, you can see that the ratio y/x is not constant meaning that they are not proportional.