Overview
On this page, we review basic properties of straight lines, including their slope and \(y\)-intercept, their graphs, as well as their equation in either slope-intercept or (preferably) point-slope form. We also discuss horizontal, vertical, parallel, and perpendicular lines.
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.
- Determine the slope of a line from either its graph or from two given points on the line.
- Write down the slope-intercept equation for a line, when its slope and \(y\)-intercept are given.
- Rewrite a given equation for a line into slope-intercept form.
- Draw the graph of a line when its slope-intercept equation is given.
- State the equation of a horizontal or vertical line through a specified point.
- Write down the point-slope equation of the line, when its slope and a point on the line are given.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Recognize from the given equations of two lines whether they are parallel, perpendicular, or neither.
- Find the equation of a line which is perpendicular or parallel to a given line, respectively.
To prepare for class
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Watch the following video (by Tyler Wallace) which gives a quick review of the coordinate plane and how to draw a straight line from its given equation:
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Watch the following video (by Tyler Wallace) which explains how we can determine the slope of a line from its graph:
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Watch the following video (by Tyler Wallace) which explains how we can determine the slope of a line from the coordinates of two points on the line:
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Watch the following video (by Tyler Wallace) which discusses how to find the slope-intercept form of the equation of a line:
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Watch the following video (by Tyler Wallace) which explains how to rewrite a given equation for a line into slope-intercept form:
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Watch the following video (by Tyler Wallace) which shows how to draw the graph of a line from its given equation:
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Watch the following video (by Tyler Wallace) which discusses the special cases of horizontal and vertical lines and how to find their equations:
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Watch the following video (by Tyler Wallace) which explains how to find the point-slope form of the equation of a line, from a given point and slope:
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Watch the following video (by Tyler Wallace) which explains how to find the point-slope form of the equation of a line, from two given points on the line:
After class
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Watch the following videos (by Tyler Wallace) which explain the relationship between the slopes of parallel or perpendicular lines, respectively, and how to use this to find their equations:
