Worth noting it's not a linear relationship - 100k immigrants do not take 50k or whatever homes that would have gone to people already there. That's because immigrants also create building companies and incentives for existing ones to build more houses, and because immigrants disproportionately work in construction and thus provide workforce to build more.

The UK experienced this when Brexit caused many Eastern Europeans to go home, and even more not to come; there's now a big construction workforce shortage and housebuilding is being held up.