Equation to draw a budget graph

Question

Say I have $50,000 in cash, and need a loan for the rest of a house.

Holding the loan-to-value constant at 80%, how can I plot the amount of remaining cash against the price of the house?

y = ...?

Sorry if this is far too easy for this site!

Answer 1

If you're just trying to get the graph of remaining cash vs the price of the house, then it's just simply

$$y=50000-\frac x5$$, where $x$ is the price of the house (with a maximum of $250$K that you can afford since you're putting $20\%$ down for the mortgage); and $y$ is the money that you have left in your pocket after putting a $20\%$ down payment.

Here's the graph generated by Wolframalpha.