To graph the ordered pairs given in the table on the coordinate plane, follow these steps:
1. Identify the Ordered Pairs:
The table provides us with these ordered pairs:
- [tex]\( (-2, 5) \)[/tex]
- [tex]\( (-1, 2) \)[/tex]
- [tex]\( (0, 1) \)[/tex]
- [tex]\( (1, 2) \)[/tex]
- [tex]\( (2, 5) \)[/tex]
2. Draw the Coordinate Plane:
Create a coordinate plane with a horizontal axis (x-axis) and a vertical axis (y-axis). Mark the origin (0, 0).
3. Scale the Axes:
Determine an appropriate scale for both the x-axis and the y-axis. Consider the range of the x-values and y-values from your ordered pairs:
- The x-values range from [tex]\(-2\)[/tex] to [tex]\(2\)[/tex].
- The y-values range from [tex]\(1\)[/tex] to [tex]\(5\)[/tex].
Choose a scale that fits these ranges comfortably. You can use increments of [tex]\(1\)[/tex] for both axes.
4. Plot Each Ordered Pair:
- For [tex]\( (-2, 5) \)[/tex], start at the origin, move 2 units to the left along the x-axis, and then 5 units up along the y-axis. Place a point there.
- For [tex]\( (-1, 2) \)[/tex], start at the origin, move 1 unit to the left along the x-axis, and then 2 units up along the y-axis. Place a point there.
- For [tex]\( (0, 1) \)[/tex], start at the origin (already at [tex]\(0\)[/tex] on the x-axis), and move 1 unit up along the y-axis. Place a point there.
- For [tex]\( (1, 2) \)[/tex], start at the origin, move 1 unit to the right along the x-axis, and then 2 units up along the y-axis. Place a point there.
- For [tex]\( (2, 5) \)[/tex], start at the origin, move 2 units to the right along the x-axis, and then 5 units up along the y-axis. Place a point there.
5. Connect the Points (if required):
If you need to show the relationship or pattern between these points, you can connect them with straight lines. In this case, it might be insightful to connect the points to visualize a parabolic shape.
6. Label the Axes:
- Label the x-axis as "Input (x)".
- Label the y-axis as "Output (y)".
7. Add Titles and Grid (if necessary):
- Consider adding a title to the graph, such as "Graph of Ordered Pairs (x, y)".
- Adding a grid can help in accurately plotting and visualizing the points, so feel free to add grid lines.
By following these steps carefully, you will have a properly plotted graph of the ordered pairs given in the table.
