# Comparing the magnitudes of the slopes of two lines

I am going over rate of change with my 8th graders tomorrow and I foresee a difficulty. I would like to see different ways to explain this for my students who have trouble with it.

In terms of magnitude, which function has the greater rate of change? $$y=−2x+1 \qquad{\text{or}}\qquad y=2x+1$$

• Sorry, in terms of magnitude. – Ash Oct 9 '16 at 16:13
• Asking which function has the greater rate of change could be misleading, as students may miss the possibility of equality or feel that it is ruled out for some reason. Currently, the question could be interpreted as a trick question. – J W Oct 9 '16 at 16:26
• In a way it is a trick question. On the actual sheet one function is a table and the other is a graph. The goal is to be able to identify the slopes and compare them. This is our first example where the rate of change is the same but with different signs. I want them to think about it first before I phrase it as "are they the same? why or why not?" but now I may do just that to help guide their thinking. – Ash Oct 9 '16 at 16:45
• Really, this isn't a question about rate of change. As currently stated ("In terms of magnitude, Which function has the greater rate of change?"), this is a question on whether they know the meaning of the word "magnitude" or not. – Daniel R. Collins Oct 9 '16 at 18:07
• Have you given the students precise definitions of "rate of change" and "magnitude"? If so, what are those definitions? (It's hard to foresee what difficulties the students will have without knowing what the words in the question will mean to them.) – Daniel Hast Nov 2 '16 at 2:23