To represent the relation given by the set of pairs [tex]\(\{(-3, 2), (5, 5), (3, 3), (3, -2)\}\)[/tex] on a graph, we need to plot each of these points on the Cartesian plane. Here are the steps to achieve this:
1. Understand Each Pair: Each pair represents a point on the Cartesian plane where the first value is the x-coordinate and the second value is the y-coordinate.
- [tex]\((-3, 2)\)[/tex]
- [tex]\((5, 5)\)[/tex]
- [tex]\((3, 3)\)[/tex]
- [tex]\((3, -2)\)[/tex]
2. Draw the Axes:
- Draw a horizontal line to represent the x-axis.
- Draw a vertical line intersecting the x-axis at the origin [tex]\((0,0)\)[/tex] to represent the y-axis.
3. Mark the Points:
- Begin with [tex]\((-3, 2)\)[/tex]:
- Move three units to the left along the x-axis (since [tex]\(x = -3\)[/tex]).
- From there, move two units up parallel to the y-axis (since [tex]\(y = 2\)[/tex]).
- Mark the point [tex]\((-3, 2)\)[/tex].
- Next, [tex]\((5, 5)\)[/tex]:
- Move five units to the right along the x-axis (since [tex]\(x = 5\)[/tex]).
- From there, move five units up parallel to the y-axis (since [tex]\(y = 5\)[/tex]).
- Mark the point [tex]\((5, 5)\)[/tex].
- Next, [tex]\((3, 3)\)[/tex]:
- Move three units to the right along the x-axis (since [tex]\(x = 3\)[/tex]).
- From there, move three units up parallel to the y-axis (since [tex]\(y = 3\)[/tex]).
- Mark the point [tex]\((3, 3)\)[/tex].
- Finally, [tex]\((3, -2)\)[/tex]:
- Move three units to the right along the x-axis (since [tex]\(x = 3\)[/tex]).
- From there, move two units down parallel to the y-axis (since [tex]\(y = -2\)[/tex]).
- Mark the point [tex]\((3, -2)\)[/tex].
4. Label the Axes: Label the x-axis and y-axis appropriately to show the positions of the points accurately.
5. Plotting the Points:
- You should see the following points:
- [tex]\((-3, 2)\)[/tex] on the left side
- [tex]\((5, 5)\)[/tex] on the far right upper corner
- [tex]\((3, 3)\)[/tex] towards the right upper part
- [tex]\((3, -2)\)[/tex] below the x-axis directly beneath [tex]\((3, 3)\)[/tex]
Once all these steps are done, your graph should have the four points plotted correctly representing the relation [tex]\(\{(-3, 2), (5, 5), (3, 3), (3, -2)\}\)[/tex].
