To determine the equation of the line \( y = mx \) through the origin that describes the proportional relationship shown in the graph, we need to identify the slope \( m \) based on the provided options:
A. \( y = \frac{1}{2}x \)
B. \( y = x \)
C. \( y = 2x \)
The slope \( m \) in each option represents the ratio of change in \( y \) to the change in \( x \).
- If the graph shows a line that goes up at a rate where \( y \) is half of \( x \), then the correct equation would be A \( y = \frac{1}{2}x \).
- If the graph shows a line where \( y \) equals \( x \), then the correct equation would be B \( y = x \).
- If the graph shows a line that rises twice as fast as \( x \) (i.e., \( y \) is twice \( x \)), then the correct equation would be C \( y = 2x \).
Without seeing the actual graph, we can't definitively choose an option. However, you can determine the right answer based on the slope you observe in the graph. If you can provide that information, I can help you identify the correct equation!