Converting the relationship between two chromaticity coordinates into a linear function

Question

I have the following equations which each represent a chromaticity coordinate:

$x = \frac{r^{2.4}}{r^{2.4} + (0.4r + 0.6b)^{2.4} + b^{2.4}}$

$y = \frac{b^{2.4}}{r^{2.4} + (0.4r + 0.6b)^{2.4} + b^{2.4}}$

where $r = [0,1]$ and $b = [0,1]$

which produces the following graph: graph of relationship between two chromaticity coordinates

How can I express the relationship between these two chromaticity coordinates as a linear function in terms of x? In other words, what is the equation for the line in the graph?

Thank you!

Answer 1

Here is how I express my curve in the form of parametric equations in terms of $t$:

$x = \frac{t^{2.4}}{t^{2.4} + (0.4t + 0.6(1-t))^{2.4} + (1-t)^{2.4}}$

$y = \frac{(1-t)^{2.4}}{t^{2.4} + (0.4t + 0.6(1-t))^{2.4} + (1-t)^{2.4}}$