1. **State the problem:** We need to identify which equation corresponds to the graphed line. 2. **Analyze the graph:** The line passes through the origin (0,0) and slopes upward to the right, indicating a positive slope and zero y-intercept. 3. **Recall the slope-intercept form:** The general form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Check each option:** - A. $y = 2$ is a horizontal line, slope 0, y-intercept 2. - B. $y = -\frac{3}{2}x + 4$ has negative slope and positive intercept. - C. $y = -\frac{3}{2}x - 4$ has negative slope and negative intercept. - D. $y = \frac{3}{2}x + 4$ has positive slope but y-intercept 4. - E. $y = \frac{3}{2}x - 4$ has positive slope but y-intercept -4. 5. **Match with graph:** The line passes through the origin, so $b=0$. Only option with $b=0$ and positive slope is none of the above explicitly, but since the line passes through origin and slopes upward, the equation must be $y = mx$ with $m>0$. 6. **Conclusion:** None of the options exactly match $y=\frac{3}{2}x$ (positive slope, zero intercept). Since the line passes through origin and slopes upward, the closest is a line with positive slope and zero intercept. **Final answer:** The graphed line corresponds to $$y = \frac{3}{2}x$$ which is not listed exactly but matches the description of the line passing through origin with positive slope.