Quasilinear utility

In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Formally, for example, such a utility function could be written $$U(x,y) = u(x) + by, where $$b is a positive constant. Then if $$u'(x)>0 and $$u"(x)<0, the indifference curves are parallel. Because in standard consumer theory utility functions are ordinal, one may assume without loss of generality that $$b = 1.