# Multicollinearity over intervals

You have multicollinearity when you have 2 variables $(X_1, X_2)$ that have a relationship, $X_1=a+X_2$ where $a$ is constant. My question is: is there still a multicollinearity issue if $a$ is not constant, $X_1=X_3+X_2$? For example your testing children and you have their birthday and the date of the test, so date of test $-$ birthday$=$age at test. Could you use age at test and birthday in a regression model? I ask because there would be a perfect correlation for one test interval, but as you add test intervals the correlation decreases.