If the slope of a simple linear regression line is 0, then the predicted value of the dependent variable is the same for every value of the independent variable, so there is no relationship. When we estimate the slope from data we’ll likely almost always get a slope that is not 0. Carrying out inference for the slope will allow us to conclude whether there really is a linear relationship, or whether the fact that the estimated slope isn’t 0 is just due to chance.
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Notes on the video: Inference for the Slope