The graph of the equation y = x√y represents a specific relationship between the variables x and y. This is not a linear equation, so it will not form a straight line. Instead, it illustrates a curve when plotted on a Cartesian coordinate system.
To visualize this, you can rearrange the equation into a more familiar form. Starting with y = x^2, we can see that for every value of x, the value of y is the square of x. This means:
- When x is 0, y is also 0.
- As x increases, y increases more rapidly since it is squared.
- For negative values of x, y will also be positive due to squaring.
This results in a parabolic curve that opens upwards, centered on the y-axis. Essentially, for each positive or negative value of x, there is a corresponding positive y value, depicting the typical U-shape of a parabola.
To summarize, the graph of y = x^2 is a parabola that visually represents the relationship between x and y, creating a curving line that extends indefinitely in both the left and right directions as well as upward.