Week 3: Graphing Equations—Linear Functions and Systems of Equations

Graphs are often used to visualize the relationship between two variables. You will find graphs in media, academic, and professional life. Relationships, such as those between wind speed and temperature, supply and demand, or sales and time of year, can be difficult to interpret if looking at tables of numbers. A graph can clearly show that sales of winter coats dip in June while ice cream sales rise.

For example, when comparing two cell phone companies you might find:

• Company 1 charges $40 a month plus $15 per gigabyte (g) of data. The plan’s total cost can be modeled as follows:

  C= 40+15g

  Where C is Company 1, 40 is the monthly cost, and 15g is the surplus charge of $15 for each additional gigabyte of data.

• Company 2 charges $60 a month plus $10 per gigabyte of data. This plan can be modeled with the following equation:

  C=60+10g



Photo Credit: Note. This graph is for educational purposes only.

Both equations can be graphed to visualize the total charges of each company based on how many gigabytes of data you anticipate using. When determining which company’s offering is the best choice for you, it might be useful to determine at what point the cost of the two companies is equal. Solving systems of equations will reveal this solution.

This week, you will examine how to plot points in a rectangular coordinate system and graph equations and functions. You will also explore how to solve application problems using systems of equations.

Discussion: Changing Technology

Technology changes every minute of every day. Not being able to access the web instantly seems almost impossible for the next generation to fathom. Most children born today will never know the sound of a dial-up modem. Changes in technology can be measured using the basic premise of slope or rate of change to examine patterns. Chris Anderson explores the life of technology in a dated 2004 TED Talk. Be aware the data is old (and you may get a chuckle out of some of it), however, the concept of measuring the life of technology is not.

For this Discussion, you examine the components and patterns of a graph and explore interpretations that can be derived from the placement of variables on a graph.

To prepare for this Discussion:

• Review the video on technology’s long tail and select one of the graphs presented in the video.
• Reflect on what the graph you selected shows, including what variables are on the x- and y-axis and what patterns are displayed on the graph. Be sure to consider all the key points as presented on the graph.
• Think about two points on the graph you selected. Consider how you would write these points, as ordered pairs, and determine the slope between the two points. It is recommended that you pause the video to make it easier to identify two points.
• Approximate the y-intercept of the graph you selected. If the y-intercept is not visible on your graph, select a reasonable value for it, and think about why you chose it.
• Think about how you would write an equation for the line in the form of y=mx+b using the y-intercept (b) and slope (m), and how you would interpret the slope as a rate of change, including what it means in terms of change for both variables.
• Consider a prediction you might make for the year 2025 on your graph, using the slope value as a rate of change, and think about whether or not you feel the prediction is reasonable. Why
  

below is the video and transcript that need to be referenced and cited:

1. Anderson, C. (2004, February). Technology’s long tail [Video]. TED Conferences. https://www.ted.com/talks/chris_anderson_technology_s_long_tail
Note: The approximate length of this media piece is 14 minutes.

Technology’s Long Tail Transcrip

2. https://www.youtube.com/watch?v=Cddn2OlcflA&t=4s