Graph the line that passes through the coordinates below and determine which statement is true.

Question

1 2 3 4 5 6 7 8

A.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.

Answer 1

To determine if the line represents a proportional relationship, we need to see if there is a constant rate of change between the points. Let's calculate the rate of change between the first two points:

Rate of change = (4-2)/(3-1) = 2/2 = 1

Now let's calculate the rate of change between the second two points:

Rate of change = (6-4)/(5-3) = 2/2 = 1

Again, let's calculate the rate of change between the third set of points:

Rate of change = (8-6)/(7-5) = 2/2 = 1

Since the rate of change is the same for all pairs of points, the line represents a proportional relationship.

However, the line does not pass through the origin (0,0), so the correct statement is:

C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.