Question

A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

The line represents a direct variation because = negative StartFraction 4 Over 3 EndFraction equals StartFraction 4 Over 3 EndFraction.
The line represents a direct variation because it is horizontal.
The line does not represent a direct variation because it does not go through the origin.
The line does not represent a direct variation because –4(3) ≠ 4(3).

Answer 1

To determine whether the line drawn through the points (-4, 3) and (4, 3) represents a direct variation, we need to understand the definition of direct variation. A relationship exhibits direct variation if it can be expressed in the form \( y = kx \), where \( k \) is a constant. One key characteristic of direct variation is that the line must pass through the origin (0, 0).

Now, looking at the points (-4, 3) and (4, 3):

1. The y-coordinates of both points are constant at 3, meaning the line is horizontal.
2. Since the list of points does not include the origin (0, 0), the line does not pass through the origin.

Based on that understanding, the correct answer would be:

**The line does not represent a direct variation because it does not go through the origin.**