Online College Courses for Credit

Slope questions answered

Slope questions answered

Author: Christopher Danielson

To answer common student questions about slope and first differences.

This brief packet consists of a short video using student questions and responses to an in-class task to address common questions about slope and first differences.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

37 Sophia partners guarantee credit transfer.

299 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 32 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.



In class, I occasionally ask students to list out things they know, things they want to know and things they have learned about a topic (this is referred to as a "KWL" among educators, for Know, Want to know, Learned).

We recently did a KWL on slope in College Algebra. I noticed that various students did an excellent job of addressing each others' questions in the "want to know" part through their "know" and "learned" responses.

This brief packet consists of a video showing students' questions and answers; the video concludes with a final answer from me.

Learners should be familiar with the concept of "first difference," which is a quick tool for analyzing change in function tables. The idea is not explained in this packet, but it is demonstrated at the end of the video.

Students' questions and answers on slope

This video uses student responses to a classroom task to ask and answer each others' questions. It finishes with a brief instructor explanation of the relationship between first differences and slope.


So slope is a rate of change (such as velocity). Slope is the ratio of the change in y to the change in x. And first differences analyze change in y. When the change in x is 1, then the first differences and the slope are identical.

First differences are a particularly useful tool when presented with a table of data. And they are especially helpful when the table is non-linear. Non-linear functions technically do not have slopes. But we can still compute first differences and look for patterns that tell us about the behavior of the function.

And first differences are an important precursor to the calculus topic of derivative.