Any 4 points in the Cartesian plane determine a unique equation that is of degree at most three (i.e., a "cubic" equation). It is, of course, possible that the 4 points actually lie on a degree two ("quadratic"), a degree one ("linear"), or a degree zero ("constant") equation. However, if the 4 points do not lie on a constant, linear, or quadratic curve, then they will like on a unique cubic curve.
In general, N points will determine a unique curve of degree at most (N-1).
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y= ax^3+bx^2+cx-42, assuming the point was (0, 42)
By the process of plotting.
Graph it (the equation).
The coordinates of every point on the graph, and no other points, are solutions of the equation.
To graph an equation that is not in slope-intercept form, you can use the process of finding points on the graph and plotting them. Choose a few x-values, plug them into the equation to find the corresponding y-values, and plot those points on the graph. Then, connect the points with a smooth line to complete the graph.