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

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?

• 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:

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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.

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