Overview
On this page, we discuss linear functions, a simple yet very important type of function.
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.
- Recognize whether a given function is a linear function or not.
- Given the point-intercept equation of a function, draw it by quickly finding two points and connecting them.
- Recognize from the slope of a linear function whether it is increasing, decreasing, or constant.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Given two points, find the equation of the linear function whose graph passes through them.
- Given one point and the slope, find the point-slope form of the equation of the linear function whose graph passes through them.
- Convert the equation of a line given in point-slope form to slope-intercept form.
- Quickly recognize (or write down) the equation of a horizontal or vertical line.
- Identify whether two given straight lines are parallel, perpendicular, or neither.
To prepare for class
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Watch the following video (by mathantics, 13m23s) which reviews linear functions and their graphs, including the slope and \(y\)-intercept:
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Watch the following video (by mathantics, 12m) which reviews how to calculate the slope of a line from two given points (also explaining the idea of “rise over run”), and how to find the distance of the two points:
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Watch the following video (by Mathispower4u, 3m20s) which reviews how to recognize if a given linear function is increasing or decreasing :
After class
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Watch the following video (by Khan Academy, 6m06s) which explains how to quickly write down the equation of a straight line with given slope passing through a given point, usint the point-slope form \(y-b=m(x-a)\) f the equation of a line, and how to convert this form into point-intercept form \(y=mx+b\):
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Watch the following video (by eHowEducation, 2m) which reviews the equations of horizontal and vertical lines:
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Watch the following videos (the first by Nerdstudy, 5m34s, and the second by Mario’s Math Tutoring, 2m57s) which explain and show examples of how to recognize whether two lines are parallel, perpendicular, or neither:
