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This study is about the spatial demands made by graphs and about the ability of young children to cope with these demands. We wanted to answer two questions: (1) whether children can coordinate spatial information from two axes, and (2) whether the fact that they have to extrapolate non-perpendicular lines in graphs causes them particular difficulty. Sixteen six- and 16 nine-year-olds were asked to extrapolate imaginary lines in a graph-like task in order to find the position on one axis of a graph corresponding to a given position on the other axis. In addition to these axis-to-axis extrapolations, they were given separate line-to-axis and axis-to-line problems requiring the extrapolation of only one line. The older children made significantly smaller errors than the younger ones, but on the whole both age groups made accurate extrapolations in all three types of problem. Most importantly the errors in the axis-to-axis condition were not significantly different from the mean summed errors in the other two conditions (line-to-axis and axis-to-line). This shows that children do not experience difficulty with the axis-to-axis condition over and above the difficulty of extrapolating two single lines. We found no evidence that the non-perpendicularity of the lines which the children had to extrapolate caused them any particular difficulty. We concluded that young children have a more adequate understanding of rectangular coordinate systems than has been evident from their performance in other tasks and that young children can in principle cope with the spatial demands made by graphs surprisingly well.