Li believes that the graph shows a direct variation.

Question

On a coordinate plane, a line goes through points (0, 1) and (2, 0).

Why is Li incorrect in saying that the graph shows a direct variation?
The graph does not have a constant rate of change.
When the x-value is 0, the y-value is 1.
The slope is negative.
The relationship is proportional.

Answer 1

Li is incorrect in saying that the graph shows a direct variation because:

When the x-value is 0, the y-value is 1.

In a direct variation, the relationship between \( y \) and \( x \) can be described by the equation \( y = kx \), where \( k \) is a constant. For this equation to hold true, when \( x = 0 \), \( y \) must also equal 0. In the graph provided, the point (0, 1) indicates that when \( x = 0 \), \( y = 1 \), which shows that there is not a direct variation. Therefore, the relationship is not proportional because a direct variation must pass through the origin (0, 0).