Hi everyone! Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 2: Lines and Functions
Topic. This lesson covers Session 2: Lines and Functions
- Review basic properties of lines.
- Develop a conceptual understanding of functions.
WeBWorK. There is one WeBWorK assignment on today’s material:
- Lines Review
Additional Video Resources.
Question of the Day: What is the meaning of the “slope” of a line?
Lines, slope and intercepts
In this section, we review a topic you have seen before: lines. We will work through some examples below, but if you have questions or need help with any of the ideas about lines I highly recommend taking a look at these additional video resources. For example: what is the slope? What are the intercepts (x- and y-)? How do I find them? What is the slope-intercept form of a line? What is the point-slope form of a line?
Important facts about lines
- The slope of a line passing through two points and is
- A line with slope that passes through the point will have equation:
called the point-slope form of the line.
- The x-intercept of a line is the point where the line crosses the x-axis.
- The y-intercept of a line is the point where the line crosses the y-axis.
- A line with slope and -intercept will have equation:
called the slope-intercept form of the line.
- If two lines are parallel, their slopes are equal
- If two lines are perpendicular, their slopes are negative reciprocals:
- Find an equation of the line passing through the points and
- Find the slope, y-intercept, and graph
VIDEO: Example 1 – Equations of lines
Video by Irania Vazquez
What is a function?
Every once in a while you run into an idea in math that is so big, and so basic… One of these ideas was numbers (you ran into this one at a very young age). Another of these ideas is functions. In later lessons, you will be learning a lot technicalities about functions – but for today, we really want you just to understand the big idea. What is a function?
This presentation gives an introduction:
And this video provides an introduction along with several examples
VIDEO: Introduction to Functions
Video by Irania Vazquez
Good job! You are now ready to practice on your own – give the WeBWorK assignment a try. If you get stuck, try using the “Ask for Help” button to ask a question on the Q&A site.