Choose 5 ordered pairs whose first component is the opposite of the second component. Plot these points and connect them. What kind of figure do you get? In what quadrants does the figure lie?
Did you try to do this with a few points?
e.g.
(6,3) ----> (-6,3)
(-2,5) ---> (2,5)
..... try some more, then plot them
What did you notice?
or, how about
(2,-2)
(-2,2)
(1,-1)
(-1,1)
To find five ordered pairs where the first component is the opposite of the second component, we can follow this process:
1. Let's assume the first component is "x" and the second component is "y".
2. Since the first component is the opposite of the second component, we can write the equation as: x = -y.
3. Now, we can choose different values for "y" and calculate the corresponding values for "x".
Let's choose different values for "y" and calculate "x":
For y = 1, x = -1
For y = 2, x = -2
For y = 3, x = -3
For y = 4, x = -4
For y = 5, x = -5
So, the ordered pairs are: (-1,1), (-2,2), (-3,3), (-4,4), (-5,5).
Now, let's plot these points on a coordinate plane and connect them:
Coordinate Plane:
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Points: (-1,1), (-2,2), (-3,3), (-4,4), (-5,5)
Connecting these points, we get a straight line that passes through the origin (0,0). This line is in the form of y = -x.
The figure obtained by connecting these points is a straight line that extends infinitely in both directions. It passes through the origin and has a slope of -1.
Since the line passes through the origin (0,0), it lies in all four quadrants of the coordinate plane.