Graphing

= = Marked June 7th



**ALL YOU NEED TO KNOW!** 

**Graphing** This type of graph was named after a mathematician, Rene Descartes. It is a system of coordinates for plotting points where there are negative numbers, positive numbers and an origin. This is called a Cartesian Plane. __Example:__



** Scatter Plot ** A type of graph where it displays values between two related topics. The data can be displayed with a large amount of points. __Example:__



**Bar Graph** A type of graph with rectangular bars to represent values. (Can have vertical or horizontal bars). __ Example: __



**

Line of Best Fit (LOBF) -The line that fits best -The the line should be as close as possible to all the data points -The furthest data point is not included when you are making your line of best fit (the outlier) -There doesn't have to be a equal amount of dots on each side of the LOBF ** __Example:__



__How to Create a Bar Graph__

Bar Graphs are used to compare data between two or more things. 1. On graph paper, draw a right angle whatever size that will fit the data up to the highest amount on each axis 2. At the very end of the horizontal line label it x and draw an arrow head at the end of it. Do the same for the vertical line but label it y (these are the x and y axis). 3. Label the x axis along the bottom- horizontal (ex. Months, Age, Numbers, etc.) 4. Label the y axis along the side- vertical (use the numbers that are needed to measure and represent the data correctly) 5. Graph the bars and label them if they are different sets of data (or do a coloured legend) 6. Create a title for the top of your graph. It should look something like this:

TITLE
 * __Double Bar Graphs__ **

You could also use a double bar graph, which shows the comparison of two things that are related.

__**Line Graphs**__

Line graphs show the change of data over a period of time. To make a line graph plot the relationship between two or more variables and then connect the data points.

__**Double Line Graphs**__ Double line graphs are also used to show change in data over a period of time, but are used to compare more than one set of data.



__How to Create a Scatter Plot Graph Remember: *DO NOT CONNECT THE DOTS* __  1. Draw a right angle (for the x and y axis) on graph paper. 2. At the very end of the horizontal line label it x and draw an arrow head at the end of it. Do the same for the vertical line but label it y (these are the x and y axis). 3. Label the x and y axis along the lines. 4. Now graph your points on the graph by plotting the points that you have read from the set (e.x. (3,6) <--- 3 goes along the x axis, 6 goes along the y axis- (x,y) 5. Then if needed (if you have different sets of data), create a legend off to the right hand side. 6. Create a title for the top of the graph. Your scatterplot should look something like this:



__ How to Create the Line of Best fit __  Now that you know how to draw a scatter plot, you need to know how to create a line that best represents the data.... a "LINE OF BEST FIT" or (LOBF for short)

1. Draw a straight line through the points (make sure it goes through as many points as possible). Do no include the outlier which is the point on a graph that is different than the trend of the rest of the data. It is usually found far from all the other points of data. 2. At the end of the line put arrow heads, telling you that the lines keep going on, and if given an equation, label the line with the equation. 3 . Your line of best fit should look something like this:

 __ <span style="font-family: Impact, Charcoal, sans-serif; color: #1e5fa9; font-size: 25px;">How to Make a Cartesian Plane __

<span style="text-align: left; display: block; font-family: Arial, Helvetica, sans-serif; color: #2a71b2; font-size: 15px;">1. On graph paper, draw two equal lines that intersect at 90 degrees, and label your x axis (the horizontal line) and your y axis (the vertical line) with arrows at the end (not shown in picture). 2. The right side of your horizontal line after the origin start at 1 and keep going up by positive numbers as well as the top of the vertical line. 3. The left side of the horizontal line starts at -1 and are negative numbers, and the bottom of the vertical line is negative as well. 4. It should look something like this:

EXAMPLE: If you wanted to graph a line then you need coordinates to a point. Let's use (3,-5). It would look like this:

If you wanted to make a line then you would need to add coodinates to another point. Let's use (6,-1) The next point and line would look like this:

The quadrants are labeled as:



__What You Need On A Graph__ 1) Title 2) Scale 3) Labeled Axis 4) Data Points (Dots) 5) Line of Best Fit (Optional)

<span style="text-align: center; background-color: #ffffff; font-family: Georgia, serif; color: #ff0043; font-size: 140%;">__ Graphing Linear and Non-Linear Relations __ To graph linear and non-linear relations you need to create a table of values, x being -2, -1, 0, 1, and 2. Then you place the dots, draw a line of best fit, add arrows and label the lines with equations. Example: Construct a table of values for y = x - 5 __first dot__ x=-2 y= x-5 y= -2 -5 y= -7
 * **X** || **Y** ||
 * **-2** || **-7** ||
 * **-1** || **-6** ||
 * **0** || **-5** ||

** Then you would graph this table of values on a cartesian plane. The points would be as they are above in this format: ** <span style="font-family: Georgia, serif; color: #ef3206; font-size: 130%;">



<span style="text-align: center; display: block; font-family: Impact, Charcoal, sans-serif; color: #0014ff; font-size: 25px;">__Distance/Time Graphs__ Using a graphing calculator and a radar/motion sensor you can create a Distance/Time Graph. These show how far away an object is if it is moving, and how fast it is moving and in what direction.



The further you go away from a motion sensor, the higher the line gets on the graph. The longer it takes you to walk that distance, the further over to the right the line will be. In some situations, you will be asked to explain what is happening in this type of graph. Here is how you would describe this:

__**Example:**__ Johnny starts standing still in front of the motion sensor. He slowly walks away from it, 10 metres in 6 seconds. He stops for 5 seconds to tie his shoe, and then turns around and comes back towards the motion sensor, moving back 10 metres again, but took 7 seconds. (assuming that the last line is straight on the graph)

__ CORRELATION AND RELATIONSHIPS __

Relations within graphs can be positive (going up from left to right) or negative (going down from left to right). It will also be classified as stong or weak. Strong is when the data points are all close together, and weak when the dots are further away from each other.

__You could have a:__ Strong positive correlation Weak positive correlation Strong negative correlation Weak negative correlation

Connections To the Real World:
If you ever want to be a teacher, you will need to know how to make, and teach people how to create a graph. In the business world graphs are used a lot to get points across like how much money the company is making or how the company's stocks are doing in the stock market. You can also use graphing during polls, where they compare the amount of votes for each candidate. __ Graphing Videos __

In this video you will learn how to graph a line determined by an equation's slope. Visit the SLOPES page for more information.

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Edited By: Jenn, Jade, Trevor, and Emma

"cartesian." __Think Quest__. 17 Dec. 2008 <http://library.thinkquest.org/C0110248/geometry/graphics/cartesian1.jpg>. 17 Dec. 2008 <http://upload.wikimedia.org/wikipedia/commons/6/63/Distance-time_graph_example.png>.