Overview
On this page, we discuss how many real world situations can be described using linear functions, and how we can then use this to answer specific questions about these situations.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Given a real world situation, decide whether it is reasonable to assume that it can be modeled by a linear function.
- Find the linear function describing a given real world situation, by finding the slope and writing out the point-slope form of the linear function, and then converting this to slope-intercept form.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Directly find the linear function describing a given situation when the \(y\)-intercept and slope are known.
To prepare for class
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Watch the following video (by MyWhyU, 13m09s) which shows how to describe a real-world situation by a linear function (and when this is reasonable), and how to then use this to answer specific questions (you may choose to fast-forward the first 2 minutes):
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Watch the following video (by LawrenceAcademy Math) which shows an example of finding a linear model for a given word problem:
After class
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Watch the following video (by Khan Academy, 4m57s) which shows how one can sometimes directly determine the linear equation for a given situation:
