find the graph for this direct variation equation. y = 2x

Explanation:

Step1: Recall Direct Variation Graph Properties

A direct variation equation ( y = kx ) (here ( k = 2 )) is a linear equation passing through the origin ((0,0)) with slope ( k ). The slope ( 2 ) is positive, so the line should rise from left to right.

Step2: Analyze Each Graph

• First graph: Does it pass through ((0,0))? Let's check. The line seems to have a y - intercept not at 0 (or slope less than 2).
• Second graph: It has a negative slope (falls from left to right), so it can't be ( y = 2x ) (positive slope).
• Third graph: Passes through the origin ((0,0)) and has a positive slope (rises from left to right), consistent with ( y = 2x ) (slope ( 2>0 )).

Answer:

The Right Graph