[MUSIC PLAYING] Let's look at our objectives for today. We'll start by defining the coordinate plane. We'll then discuss how we can talk about coordinate points on the coordinate plane. We'll introduce a type of graph called a scatterplot. And finally, we'll do an example analyzing a scatterplot. Let's talk about the coordinate plane. The coordinate plane is a two-dimensional surface used to plot and identify points. The coordinate plane consists of a horizontal number line called the x-axis and a vertical number line called the y-axis.
Both the x-axis and the y-axis have a positive and negative side and both have a center at 0. The centers of the x and y-axes intersect at a point in the coordinate plane called the origin. The origin is at 0 on both the x-axis and the y-axis. The x and y-axes divide the coordinate plane into four quadrants. In quadrant 1, x and y are both positive. In quadrant 2, x is negative and y is positive. In quadrant 3, the x and y are both negative. And in quadrant 4, x is positive and y is negative.
Now let's look at coordinate points on a coordinate plane. All points on the coordinate plane can be indicated by an x value and a y value. These two values form a coordinate pair and is written as x,y. The point at the origin is represented by the coordinate pair 0, 0. Starting at the origin, the first coordinate indicates how far to move in the horizontal direction along the x-axis. And the second coordinate indicates how far to move in the vertical direction along the y-axis.
For example, the ordered pair 3,5 is 3 units in the positive x direction and 5 units in the positive y direction, both from the origin. It's also where x is 3 and y is 5. The ordered pair negative 2, negative 6 is two units in the negative x direction from the origin and 6 units in the negative y direction from the origin. It is also the point where x is negative 2 and y is negative 6.
The ordered pair negative 1, 4 is one unit in the negative direction and four units in the positive y direction. It's also where x is negative 1 and y is 4. In the ordered pair 6, negative 5, is 6 units in the positive x direction and 5 units in the negative y direction. It's also where x is 6 and y is negative 5.
Now let's look at a type of graph called a scatterplot or diagram. A scatter diagram is the collection of points on the coordinate plane used to represent data. Coordinate points in ordered pairs in scatter diagrams form a relationship between two variables. Scatter diagrams are used to display various types of data in science, psychology, sociology, and statistics. Being able to read and interpret graphical information is important in these areas of study.
Let's look at an example of a scatter diagram and analyze the data represented. The arm spans and heights of 10 people were measured and the data was plotted on the scatter diagram. The x-axis represents the values of the x variable, arm span, which was measured in centimeters, and the y-axis represents the values of the y variable, height, which was also measured in centimeters. Each point on the graph represents the arm span in height for one person.
For example, this point represents the person who had an arm span of 165 centimeters and a height of 166 centimeters. This point here represents the person who had an arm span of 157 centimeters and a height of 160 centimeters. In addition, we can use the scatterplot to answer, what was the height of the person with an arm span of 156 centimeters? To do this, we identify the point where the x value was 156. And we could see that that point has a y value of 159 centimeters. So the person's height was 159 centimeters.
We could similarly use the scatterplot to answer, what was the arm span of a person with a height of 157 centimeters. To do this, we identify the point where the y value was 157 and we see that point has an x value of 160. So their arm span was 160 centimeters.
Let's go over our important points from today. Make sure you get these in your notes so you can refer to them later. The coordinate plane consists of a horizontal number line called the x-axis and a vertical number line called the y-axis. The centers of the x and y-axes intersect at a point in the coordinate plane called the origin.
The origin is at 0 on both the x-axis and y-axis. The point where the origin is is represented by the coordinate pair 0, 0. A scatter diagram is a collection of points in the coordinate plane used to represent data. Coordinate points in ordered pairs in scatter diagrams form a relationship between two variables.
So I hope that these important points and examples helped you understand a little bit more about graphing points on the coordinate plane. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.
A two dimensional surface used to plot and identify points.
A collection of points in the plane used to represent data.