Deriving equation for income offer curve

Sorry if this is a basic question, however I have no idea on how to derive an equation for an income offer curve. All the explanations I'm getting is the graphical one where you just connect the different optimum points. It would be really helpful if someone can explain how do you derive an equation for such given any utility function.

• Hint: Solve a utility maximization problem $\max_{x,y}u(x,y)$ subject to budget constraint $p_xx+p_yy\le m$. The optimal solutions, $x^*(m,p_x,p_y)$ and $y^*(m,p_x,p_y)$, are functions of income and prices. Hold prices constant (i.e. slope of budget line is constant) and plot $x^*(m)$ and $y^*(m)$. – Herr K. Sep 27 '18 at 16:21