Since and , there are points on the graphs of and where . These graphs are the special cases of where and . All points with can be found as intersections of the graph with the lines with slope . In this case, parametric equations in terms of have simple formulas.
The graph of is black. The graph of interest, where , is blue for and red for , and is the graph of a function . The intersection points with and , for , and corresponding points on , are plotted.
It is interesting to see that when is varied between 0 and 2, the graph of bows from concave up to concave down, and appears to be a line segment from to for some . The graphs of and are shown to help you decide whether the graph of for this really is straight. The special satisfies .
The case is especially interesting because then the equation is equivalent to , which has a solution and . (The slider for can take values from -2 to 5.)