One way of checking it is by slopes, because both x = -y and y = 2x +1 are straight lines only.

If y = 2x +1 were symmetrical with respect to y = -x, then y = 2x +1 should be perpendicular to y = -x. If not, then there is no symmetry.

y = -x

slope, m1 = -1

y = 2x +1

slope, m2 = 2

To be perpendicular, their slopes must be the negative reciprocals.

m2 = -1/m1

2 = -1 / -1

2 = 1

False, so the two lines are not perpendicular, and so y = 2x +1 is not symmetrical wirh respect to y = -x.

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Another way.

y = -x -------------axis of symmetry.

y = 2x +1 --------(i)

If (i) is symmetrical, when we swap the x and y into (i), we should get an equation similar or equal to (i).

-x = 2(-y) +1

-x = -2y +1

2y = x +1

y = (1/2)(x +1) -------not the same as (i), so, no symmetry.