Many metaphors in language reflect conceptual metaphors that structure thought. In line with metaphorical expressions such as 'high number', experiments show that people associate larger numbers with upward space. Consistent with this metaphor, high numbers are conventionally depicted in high positions on the y-axis of line graphs. People also associate good and bad (emotional valence) with upward and downward locations, in line with metaphorical expressions such as 'uplifting' and 'down in the dumps'. Graphs depicting good quantities (e.g., vacation days) are consistent with graphical convention and the valence metaphor, because 'more' of the good quantity is represented by higher y-axis positions. In contrast, graphs depicting bad quantities (e.g., murders) are consistent with graphical convention, but not the valence metaphor, because more of the bad quantity is represented by higher (rather than lower) y-axis positions. We conducted two experiments (N = 300 per experiment) where participants answered questions about line graphs depicting good and bad quantities. For some graphs, we inverted the conventional axis ordering of numbers. Line graphs that aligned (versus misaligned) with valence metaphors (up = good) were easier to interpret, but this beneficial effect did not outweigh the adverse effect of inverting the axis numbering. Line graphs depicting good (versus bad) quantities were easier to interpret, as were graphs that depicted quantity using the x-axis (versus y-axis). Our results suggest that conceptual metaphors matter for the interpretation of line graphs. However, designers of line graphs are warned against subverting graphical convention to align with conceptual metaphors.