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# Slope of two parallel lines

Tina says: “Two students have done this so far. Not a mistake, but still curious what these kids are thinking:”

She’s talking about the 4/6 thingy. Any ideas, people?

## 5 replies on “Slope of two parallel lines”

Well… the slope of a line parallel IS 4/6 but that is an awkward way to write this answer. Sure would like to know a bit more about this student. Looking to the questions around it to find clues as to why this answer would be presented this way and that doesn’t help either.

Students don’t think that things can be just that easy, the same number as the slope they found. It’s almost like they don’t trust the numbers. This might be their way of ensuring they aren’t having a fast one pulled over them.

Michael Paul Goldenbergsays:

What is “the 4/6 thingy”?

I think @Isquared has a point which could explain the “error,” such as it is. She fears repeating a number already in the problem. And if she is clear about slope, that’s fine. The answer isn’t wrong, as @mrdardy states.

Here’s another thought, though it’s a stretch: as the slope of the line is given as 2/3 with nothing more to go on, she might have put her finger on the point (2, 3) and then moved 2 units to the right and 3 units up (or the reverse order) and arrived at. . .(4, 6). That would be consistent with a common misunderstanding about slope, and if she exhibited that error in other places, but not in every instance, that would be something that happens rather often: kids forget that slope is a ration of change in y to change in x. Or thought the problem asked for another point the line would go through or that a line parallel to it would go through.

I think those are ‘reaches’ but not utterly ridiculous, and at least might account for the 4 & 6 here. But I am more inclined to think it is, after all, just caution about repeating numbers from the prompt. Maybe not a case of not trusting the numbers so much as not trusting her understanding or not trusting the teacher. If you’ve had a few teachers who throw “softball” questions that really are NOT softballs, it’s easy to become paranoid. ;^)

I think there’s a bit of truth in what each person has said.
My first thought was that she knew it was the same slope, but that somehow because it was a different line it couldn’t be EXACTLY the same. Equivalent is the closest idea to same, but not entirely the same. So, in a sense she is looking to express a degree of “sameness” that is not equal-ness. The slopes are equivalent, but they are not equal. 4/6 meets the criteria of equivalent, but not “the same.”
It’s interesting to me because I see this as a positive sign of mathematical thinking, although maybe not the thinking about the slope of a line. The student is grappling with parallelism and equivalence and has found that they have something in common. This response captures her perception of a degree of “sameness,” even if she lacks the precision that you’re looking for.
2₵

I don’t think we have enough information to clearly make any judgment call on “Why did this student put 4/6?” Perhaps the students have been taught that the only way to produce the slope of a line parallel is simply scale the first. So, if my first slope is (2/3), then scale by 2 to get (4/6).