Does the response depend on X?
In a normal linear model, the response has a distribution whose mean, µy, depends linearly on the explanatory variable,
Y ~ normal (μy , σ)
If the slope parameter, β1, is zero, then the response has a normal distribution that does not depend on X.
Y ~ normal (β0 , σ)
This can be tested formally with a hypothesis test for whether β1 is zero.