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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

Stop picturing tables with food on top. That's not the kind of table we're talking about here. The **tables** we are talking about are the ones you create or read with rows and columns of data. In math, you use tables to help you keep track of points for a function so you can plot the points later. For example, for the function *y* = *x*^2, we have a table like this:

x |
y |
---|---|

1 | 1 |

2 | 4 |

3 | 9 |

How did we get the information in the table from the function? We first decided to pick our *x* values of 1, 2, and 3. We then plugged in each of our *x* values into our function to evaluate it at that number to get our *y* value. We make three evaluations since we have three different *x* values. The more numbers we have in our table, the more accurate our table will be at representing our function. So, instead of having a multiplication table, you now have a function table.

So, what about in the real world? Are tables that useful in the real world to make them worth learning about and remembering? Yes, indeed they are!

If you keep your eyes and mind open, you will spot so many uses of tables in the real world. Many useful real-world tables also represent functions. But, since it's easier to grasp information from a table than it is by looking at a function, you will see a table instead of a function.

For example, think about cell phones for a minute. With most cell phone plans, you are given so many free minutes per month and then you have to pay for every minute you talk if you go over your free minutes. Your cell phone company usually represents this information in the form of a table. If you visit their website, you will see this table of information. But did you know that there is a formula behind this? Say, for example, we see a table like this one:

Plan |
Free Minutes |
Monthly Cost |
Overage |
---|---|---|---|

A | 450 | $49.99 | 40 cents per minute |

B | 700 | $89.99 | 30 cents per minute |

C | 1400 | $129.99 | 20 cents per minute |

Look at plan A. It looks pretty decent. You pay $49.99 for 450 free minutes every month and if you happen to talk more than 450 minutes, you only pay .40 cents a minute. You're probably thinking, 'how is this a function?' Let me show you.

$49.99 is our monthly cost for the first 450 minutes, so we have the function *y* = 49.99, where *y* is our monthly bill amount for the first 450 minutes or when *x* is less than 450. The .40 cents per minute is paid only when we go over 450 minutes. How will this be included?

We need to have another equation for minutes beyond 450. If *x* is our time on the phone, I have to somehow deduct 450 minutes from it before multiplying it by .40 cents. I can do that by subtracting 450 first from *x* and then multiplying by 0.40. I then need to add this amount to my $49.99 per month.

So, my equation for minutes beyond 450 will look like *y* = 49.99 + 0.40(*x* - 450). I actually have two functions, one is for minutes up to 450 minutes and another for minutes beyond 450 minutes, behind the table of information that looks so simple and is so easy to understand. Keep your eyes open and you will find even more examples of tables in the real world.

**Graphs**, visual diagrams of values, are just as useful as tables. Graphs, like tables, are visual ways to represent functions and other information. In algebra, we work with the Cartesian coordinate plane, the graph that looks like graph paper with a dark vertical line for the *y*-axis and a dark horizontal line for the *x*-axis. We plot functions using lines or curves depending on the function. We also create graphs from a collection of data points. This particular graph shows the function *y* = 10 * sin(*x*).

So, how are graphs useful in the real world? Well, there are many functions and collected data that explain processes that happen all around us, both in business and in nature. Graphs are used to present this information so that it is easier to understand. The most common graph we use in algebra is the line graph that shows data with the use of a line, such as the one you just saw.

For example, a line graph is used to show the population growth of a certain group or in a certain region using a line graph. This graph, for example, shows the world population over time.

The graph is a line graph with shading underneath. We see that the world's population has really skyrocketed in the time that we live in. Just like with scatter plots, if you keep your eyes open, you will see them in use.

So, now let's recap what we've learned. We learned that a **table** is data presented in rows and columns and a **graph** is a visual presentation of data. Both are used to present real data. You will see tables in use when shopping for cell phone plans and you will see graphs in use when you research population growth. These are just a few examples of how they are used in the real world. In algebra, both are used as visual representations of functions and data. Both tables and graphs make it easier to read the function or data and to understand it.

Utilize this lesson if you'd like to enhance your ability to do the following:

- Create and interpret a table
- See examples of tables and graphs in the real world
- Understand the ways in which tables and graphs are used in algebra
- Recognize the function of a line graph

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- Using Tables and Graphs in the Real World 5:50
- What is a Parabola? 4:36
- Parabolas in Standard, Intercept, and Vertex Form 6:15
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