I just a took really quick look at the javascript they used and it looks like they matched the lines to a limited set of line shapes based on various heights. So, if the low income part of the line is between these certain values, the medium low income between these, etc, then they show this result.

Here's a list of the possible results:

[{
key: "kindaSShaped",
sentence: "Your line looked a little bit like an S, with a gradual increase for the poorest families and a leveling off for the rich. Thatâ€™s what we guessed the first time, too. But we were wrong. Itâ€™s a straight line."
}, {
key: "underEstimatePoor",
sentence: "You underestimated the chances of college enrollment for the very poorest children. In reality, about one in four children in Americaâ€™s poorest families go to college. (You guessed around " + e.round(t[0]) + " percent.)"
}, {
key: "overEstimatePoor",
sentence: "You overestimated the chances of college enrollment for the very poorest children. In reality, about one in four children in Americaâ€™s poorest families go to college. (You guessed around " + e.round(t[0]) + " percent.)"
}, {
key: "justRightOnPoor",
sentence: "You correctly guessed that children from the very poorest families face tough odds in going to college â€“ only about one in four do."
}, {
key: "underEstimateRich",
sentence: "You underestimated the chances of college enrollment for the very richest children. In reality, about 94 percent of children from Americaâ€™s richest families go to college. (You guessed around " + e.round(t[20]) + " percent.)"
}, {
key: "overEstimateRich",
sentence: "You overestimated the chances of college enrollment for the very richest children. In reality, about 94 percent of children from Americaâ€™s richest families go to college. (You guessed around " + e.round(t[20]) + " percent.)"
}, {
key: "justRightOnRich",
sentence: "You correctly guessed the exceptionally high rates of college enrollment for children from the very richest families â€“ about 94 percent."
}, {
key: "veryStraight",
sentence: "Your line was very straight, which means you correctly guessed one of the more striking findings of this research: The relationship between college enrollment and parental-income rank is linear."
}, {
key: "kindOfStraight",
sentence: "Your line was relatively straight, reflecting one of the more striking findings of this research: The relationship between college enrollment and parental-income rank is linear."
}, {
key: "lineButNotSteepAddition",
sentence: "Your line was not steep enough: Thereâ€™s more inequality than you guessed."
}, {
key: "lineButTooSteepAddition",
sentence: "Your line was too steep: Thereâ€™s more equality than you guessed."
}, {
key: "perfectAddition",
sentence: "Your guess was extremely accurate. Is that you, <a target='_blank' href = 'http://www.rajchetty.com/'>Raj Chetty</a>?"
}, {
key: "youAreWeird",
sentence: "Weâ€™re going to be honest here: Your line was pretty odd. Did you even try?"
}, {
key: "youAreCanada",
sentence: "Your line, which was relatively horizontal, was admirable: It suggests that everyone has the same chance of going to college regardless of parental income. <a target = '_blank' href = 'http://www.nber.org/papers/w17218'>But not even Canada</a> is that egalitarian."
}, {
key: "trustFundDip",
sentence: "You guessed that there would be a small decrease in college attendance for the richest families â€“ something weâ€™ve called the trust-fund dip. It makes some intuitive sense â€“ if youâ€™re born into an extremely wealthy family, itâ€™s reasonable to think that thereâ€™s less incentive to attend college. But the trust-fund dip does not exist."
}, {
key: "youIgnoredOurNote",
sentence: "It looks as if you didnâ€™t use the free point we gave you, which may be one of the reasons you performed worse than other people."
}, {
key: "downwardSlope",
sentence: "Your line sloped downward. Did you believe that rich children were less likely to go to college than poor children? Or did you misunderstand the axis?"