Not exactly on home prices. Home prices move mostly based on the price of new home construction and overall housing demand. Increasing interest rates will slow demand and move towards a better equalization of buyers and sellers, but overall inflation will continue to drive up the cost of new construction and renovations because both the material and labor inputs now require more dollars to build (though lumber has finally dropped a bunch). Cooling off of the housing market, or even price cuts on asking prices, doesn’t mean actual final sales prices are going down at anywhere near the rate at which interest rates are going up - it means they aren’t shooting up as quickly and the market is coming back into balance which slows the rate of inflation - it doesn’t reverse it. Except for regional/ location specific outliers, the dollar value of your home in August 2022 will be higher than the dollar value of your home in January 2021 even though interest rates could easily have double over that time frame.

If your assertion were true, the cost of entry to buying a home wouldn’t be up 44% in just over a year (half the increase from the actual dollar price, and half from the increase in the cost of borrowing those dollars).

The housing bust in 2008 was caused in part by sub-prime lending that allowed investors and home buyers to pay a temporary market interest rate well below the actual market interest rate. When the teaser rates expired, the owners discovered they couldn’t actually afford their purchase. Buyers overbought the actual market which created a bubble driving up home prices. When the teaser rate expired, the bubble burst as lots of owners and investors put their now unaffordable homes on the market, voluntarily or via foreclosure, and supply > demand, so dollar prices of homes actually went down. We don’t have that issue today - the majority of new home mortgages since the crash are fixed rate, qualifications have tightened, and as a result of inflation paying an existing fixed mortgage is getting easier, not harder. There is no looming rate adjustment to drive out existing owners.

Home prices aren’t going down until there are a lot more sellers than there are buyers, and there is no indication we are anywhere near that point. If home prices were going to reverse simply because interest rates were going up, they would have actually reversed months ago. A market coming back into to balance between buyers and sellers is a good thing for the economy, but it’s not a reversal of the inflation that has already happened.