A graph of a function y = f(x) is symmetric with respect to the origin if replacing x by -x and y by -y yields the same function. For y = 10x, if we replace x by -x and y by -y, we get -y = -10x, which simplifies to y = 10x. Thus, the graph of y = 10x is symmetric with respect to the origin.
Linear functions are odd degree functions. These type of functions do not have any symmetry with respect to the either axis.
However, the function y=mx+b
where m = ±1
b = 0
does have symmetry with respect to the origin.