For positive integers a 1 ,a 2 ,⋯,a m , we determine the least positive integer R(a 1 ,⋯,a m ) such that for every 2-coloring of the set [1,n]={1,⋯,n} with n≥R(a 1 ,⋯,a m ) there exists a monochromatic solution to the equation a 1 x 1 +⋯+a m x m =x 0 with x 0 ,⋯,x m ∈[1,n]. The precise value of R(a 1 ,⋯,a m ) is shown to be av 2 +v-a, where a=min{a 1 ,⋯,a m } and v=∑ i=1 m a i . This confirms a conjecture of B. Hopkins and D. Schaal [Adv. Appl. Math. 35, No. 4, 433–441 (2005; Zbl 1091.05069)].