graphing tiles

RISP 34: Given the symbols [math]x[/math], [math]y[/math], [math]c[/math], + and = how many distinct valid equations can you find?

How many of these nine did you find? Starting with [math]c[/math] = 1, move the slider steadily. What approximate values of [math]c[/math] give rise to special cases? Can you find suitable values to make lines tangents to the curve? Can you find suitable values to make an equilateral triangle? How can you calculate the exact values of [math]c[/math] that will make these true?