Question

Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, line y=x, line y=-x, or none of these.

x+y=6

Do I have to move the y and 6 to the other side of the equations or does it not matter? Also, if I do, when I test using the equation

a^2 + # = b^2

Would it be -y^2 or just y^2?

Answer 1

This is certainly not calculus, no does either statement make sense. I suspect something is missing.

Please put the proper subject in the heading.

Answer 2

note: to check if the given equation is symmetric to x-axis or y-axis or origin (that is, y=x),,
*symmetric to x-axis: change y to -y and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to x-axis. otherwise, it is not.

*symmetric to y-axis: change x to -x and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to y-axis. otherwise, it is not.

*symmetric to origin: change x to -x and y to -y and substitute them to the given equation. if it goes back to original form, therefore, it is symmetric to origin. otherwise, it is not.

the given equation is x+y=6,, let's check for symmetry:
*x-axis (y becomes -y)
x-y=6 ==> NOT symmetric to x-axis [since it did not go back to original form, which is x+y=6]
*y-axis (x becomes -x)
-x+y=6 ==> NOT symmetric to y-axis
*origin (x and y becomes negative)
-x-y=6 ==> NOT symmetric to origin (or y=x)

you can also check symmetry by graphing the equation,,

so there, =)