The equation 2x^2 + 2y^2 = 7 represents a circle, and to express y in terms of x, it needs to be rearranged. The correct approach involves solving for y, which will yield two solutions due to the circle's symmetry, indicated by the ± symbol. The discussion emphasizes the importance of considering the graph's lower portion when selecting between the positive and negative solutions for y. Understanding the relationship between x and y is crucial for accurately representing the circle's equation. Proper algebraic manipulation will lead to the desired equation for y.