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Understanding Ordered Pairs and Relations: Graphing Real-Life Data

Explore how ordered pairs are utilized to graph real-life data in mathematics. This guide explains the coordinate system, including the x-axis, y-axis, and origin, as essential tools for locating points. Learn the definitions of x-coordinates and y-coordinates, and how to plot points on a graph using ordered pairs, illustrated step-by-step with an example. Additionally, understand the concept of relations, domains, and ranges through tables and graphs. Practice plotting your own data and interpreting the results for better comprehension.

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Understanding Ordered Pairs and Relations: Graphing Real-Life Data

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  1. 1-6 Ordered Pairs and Relations How are ordered pairs used to graph real-life data?

  2. Vocabulary • coordinate system (coordinate plane)– used to locate points in mathematics • x-axis – the horizontal number line on the coordinate system • y-axis – the vertical number line on the coordinate system • origin – is at (0,0); the point at which the number lines intersect

  3. ordered pair of numbers – used to locate any point on a coordinate plane • x-coordinate – first number of an ordered pair • y-coordinate – second number of an ordered pair • graph of an ordered pair- point on the coordinate system that corresponds to the ordered pair

  4. Coordinate System coordinate plane y-axis x-axis origin

  5. Ordered Pair x-coordinate y-coordinate

  6. Graphing an Ordered Pair Graph (4,1) on a coordinate system. Step Three: Since the y-coordinate is 1, move 1 unit up. Draw a dot. Step Two: Since the x-coordinate is 4, move 4 units to the right. Step One: Start at the origin.

  7. Practice Please visit http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i3/bk7_3i2.htm to practice plotting points. Please use your results to complete #9 in the PowerPoint Guide.

  8. More Vocabulary • relation – a set of ordered pairs • domain – the set of x-coordinates • range – the set of y-coordinates

  9. The following is an example of a relation, or a set of ordered pairs. The domain is (1,2,3,4) The range is (2,4,0,5)

  10. A relationship can be shown in several ways. • Graph • Map • Ordered Pairs   • Table 1 2 3 4 0 2 4 5

  11. Express the following relation as a table. Please review the following example:

  12. Express the following relation as a graph. Please review the following example:

  13. Please state the domain and range of the following relation: Please review the following example: Range: {0,1,3,2} Domain: {0,2,1,5}

  14. Please review the following example: • Some species of bamboo grow three feet in one day. • Make a table of ordered pairs in which the x-coordinate represents the number of days and the y-coordinate represents the amount of growth for 1, 2, 3, and 4 days. • Graph the ordered pairs. • Describe the graph. • The points appear to be in a line.

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