Question

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



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 represents 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 does not pass through the origin

Answer 1

To determine which statement is true, let’s first clarify the concept of a proportional relationship. A relationship is considered proportional if it can be represented by a line that passes through the origin (0, 0), indicating that when one variable is zero, the other variable is also zero.

Now, let's analyze the statements provided:

- **A.** The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
- This is incorrect. If the line passes through the origin, it may represent a proportional relationship.

- **B.** The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
- This statement is true if the line indeed passes through the origin and the relationship is linear.

- **C.** The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
- This is incorrect, as a line that does not pass through the origin is typically indicative of a non-proportional relationship.

- **D.** The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
- This is also true if the line does not pass through the origin, as it implies a non-proportional relationship.

Therefore, the true statements depend on whether the line passes through the origin or not.

**If the line passes through the origin, then the correct answer is B. If the line does not pass through the origin, then the correct answer is D.**

Without the specific coordinates to graph, we can't determine which one is definitively true but can explain the conditions under which each could be true.