To determine the equation of the line \( y = mx \) through the origin that describes the proportional relationship shown in graph A, we need to identify the correct proportionality constant \( m \).
Based on the options provided:
A. \( y = \frac{1}{2}x \) (This indicates that for every unit increase in \( x \), \( y \) increases by half a unit.) B. \( y = x \) (This indicates a one-to-one proportionality, where \( y \) increases by the same amount as \( x \).) C. \( y = 2x \) (This indicates that for every unit increase in \( x \), \( y \) increases by two units.)
If you are able to see graph A and can describe the slope or proportional relationship observed, you can then select the correct equation.
Without knowing the specifics of graph A, I can only suggest you choose the appropriate equation based on the steepness of the line when compared to the x-axis:
- If the line is relatively flat (less steep), it's likely \( y = \frac{1}{2}x \).
- If the line is at a 45-degree angle, then it's \( y = x \).
- If the line is steeper than that, it's \( y = 2x \).
If you provide further details about graph A, I can help you select the exact equation!