Why are (4, 6) and (6, 4) not at the same point on a grid?

Answer and Step-by-step explanation:

Notice that both these points are in the form of (x, y). "x" indicates that on the left-right axis (x axis), the point is x units away from the origin (0, 0). "y" indicates that on the up-down axis (y axis), the point is y units away from the origin.

In (4, 6), x = 4 and y = 6. This means that the point (4, 6) is 4 units to the right of the origin and 6 units up (see red dot on attachment).

In (6, 4), x = 6 and y = 4. This means that the point (6, 4) is 6 units to the right of the origin and 4 units up (see blue dot on attachment).

As can be seen, these two points do NOT coincide, so they are different.

Different translations about the origin

Step-by-step explanation:

For (4,6), you go 4 units towards right from the origin and 6 units up

For (6,4), you go 6 units towards right from the origin and 4 units up

Since the no. of units traveled in a direction are different, you land at two different points

table 3 represents a direct variation function. : )