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

Learning Outcomes.

  • Review basic properties of lines.
  • Develop a conceptual understanding of functions.

WeBWorK. There is one WeBWorK assignment on today’s material:

  1. 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 m of a line passing through two points P_{1}\left(x_{1}, y_{1}\right) and P_{2}\left(x_{2}, y_{2}\right) is m=\frac{\text {rise}}{\text {run}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}
  • A line with slope m that passes through the point \left(x_{1}, y_{1}\right) will have equation:
    y-y_{1}=m\left(x-x_{1}\right), 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 m and y -intercept (0, b) will have equation:
    y=m x+b, called the slope-intercept form of the line.
  • If two lines are parallel, their slopes are equal m_{1}=m_{2}
  • If two lines are perpendicular, their slopes are negative reciprocals: m_{1}=-\frac{1}{m_{2}}

Example 1.

  • Find an equation of the line passing through the points (4,-8) and (8,6)
  • Find the slope, y-intercept, and graph 4x+2y=2

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

Exit Question

Find the equation of the line in the graph below in slope-intercept form.

Graph of line passing through (0,-4) and (3,-3).

Answer

y=\frac{1}{3} x-4

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.