Question

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 1

No, this graph does not show a proortional relationship.

Explanation:

A proportional relationship requires that the slope linepass through the origin (0, 0). The fact that the cooordinate grid starts with the first point being at (0, 4) means that the slope does not pass through the origin and that it is not propotional.

You can check by using the slope formula (y / x) on the coordinates. (1,5) is 5/1 = 5, (2,6) is 6/2 = 3, (3,7) is 7/3 = 2.33, (4,8) is 8/4 = 2, and (5,9) is 9/5 = 1.8. The differences between the coordinates is not consistant or even. This further shows that the relattionship is not proportional.

Answer 2

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.