Question

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.

Explanation:

To determine why Li is incorrect, we recall the definition of direct variation. A direct variation relationship is represented by the equation \( y = kx \) (where \( k \) is a constant), and its graph must pass through the origin \((0,0)\).

• Analyzing the first option: The graph is a straight line, so it has a constant rate of change (slope), so this is incorrect.
• Analyzing the second option: The graph intersects the \( y \)-axis at \((0,1)\), not \((0,0)\). For direct variation, when \( x = 0 \), \( y \) must be \( 0 \) (since \( y=kx \) implies \( y = 0 \) when \( x = 0 \)). So this explains why it's not direct variation.
• Analyzing the third option: A direct variation can have a negative slope (e.g., \( y=-2x \) is direct variation), so the sign of the slope doesn't determine if it's direct variation.
• Analyzing the fourth option: The graph is not proportional (since it doesn't pass through the origin), so this statement is false.

Answer:

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