Let L_{a,b} be a line in the Euclidean plane with slope a and intercept b. The dimension spectrum sp(L_{a,b}) is the set of all effective dimensions of individual points on L_{a,b}. Jack Lutz, in the early 2000s posed the dimension spectrum conjecture. This conjecture states that, for every line L_{a,b}, the spectrum of L_{a,b} contains a unit interval.

In this paper we prove that the dimension spectrum conjecture is true. Specifically, let (a,b) be a slope-intercept pair, and let d = min{dim(a,b), 1}. For every s ∈ [0, 1], we construct a point x such that dim(x, ax + b) = d + s. Thus, we show that sp(L_{a,b}) contains the interval [d, 1+ d].