# Significant interaction but non-significant slopes?

I have conducted a moderation analysis as follows:

x (continuous independent variable, centered) m (continuous moderator, centered)
y (dependent variable)

By entering x, m, and the product of x and m (x.m, interaction factor) into simultaneous regression, I get an overall significant model, with significant regression coefficients for x (beta x=0.273), for m (beta m=0.215) and for x.m (beta x.m=-0.034), all p<0.05. I understand that this means that m is a significant moderator of the relationship between x and y.

However, when I try to plot simple slopes at high (+1SD) and low (-1SD) levels of m, both slopes are nonsignificant (unstandardized slope 0.029, t=0.314 and p=0.89 for high m, and unstandardized slope 0.1349, t=0.902 and p=0.37 for low m). I believe this means neither slope is different from zero.

My question is, does this invalidate my interaction? Should I therefore not consider m a significant moderator of y on x? If the interaction is still valid, how do I report the results of the simple slope analysis?