What information is gleaned if we reject the null hypothesis for the test of the slope of the least squres regression line?
The slope is nothing but the regression coefficient. The conclusion is that the concerned variable characteristics are not linearly related or the regression line is not of "best fit"
I have modified the question as follows:
What do we conclude when the null hypothesis regarding the slope of the regression equation is rejected:
Rejecting the null hypothesis implies the regression line is not a good fit.