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