Most of the statistics material suggest that when the interaction term is significant, even though the main effect term is not significant, we still keep the main effect term.
For example: $$z = a + b\cdot x + c\cdot y + d\cdot xy$$
$x$ is continuous while $y$ is categorical (two levels, $y_1$ and $y_2$). $z$ is continuous. The linear model fitted has a significant $xy$ term, intercept term and $x$ term but non-significant $y$ term.
Can I reduce the model to $z = a' + b'\cdot x + d'\cdot xy$ ? Interpretation is that for level $y_1$ and level $y_2$, they have the same intercept but different slope.