Linear Functions and their Inverses

The blue sliders allow you to change the gradient and y-intercept of the function, shown by the blue line. The red line shows the inverse function. The purple dot marks the point where the two lines intersect.
What do you notice about the points of intersection? Will this always happen? Why/why not? What does this tell you about the function and its inverse? If f(x)=mx+c, the what is the general form of the inverse function, f'(x)? Find a function and its inverse that intersect at a specific point, e.g. (3,3). What is the solution set for all functions that intersect with their inverse at that same specific point? What is the solution set for all functions that intersect with their inverse at a general point (n, n)? Using the general form of a linear function, f(x), what conditions are necessary for it to be self-inverse? Demonstrate the different solutions for self-inverse linear function.