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

Question

(1 ,2), (3, 4), (5, 6), (7, 8)

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

Answer 1

To determine which statement is true regarding the line passing through the given coordinates (1, 2), (3, 4), (5, 6), and (7, 8), we first check if a proportional relationship exists.

A proportional relationship can be defined by the equation \( y = kx \), where \( k \) is a constant. For a line to represent a proportional relationship, it must pass through the origin (0,0).

1. Analyze the given coordinates:

   • (1, 2)
   • (3, 4)
   • (5, 6)
   • (7, 8)

2. Check if they pass through the origin:

   • None of the provided points go through the \( (0, 0) \).
   • Therefore, the line described by these points does not represent a proportional relationship.

3. Evaluate the slope:

   • The points plot a line that keeps increasing at a consistent rate, which indicates a linear relationship. However, this is not proportional since they do not pass through the origin.

4. Decide on the correct statement:

   • Since the line does not pass through the origin, it does not represent a proportional relationship.

Thus, the correct answer 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.