simple linear regression

Given that, a simple linear model is y=B0+B1x, if we believed that an increase of 1 unit of X should be expected to reduce 3 units of y. How can I set the hypothesis to test the y will reduce less than 3 units? Is it H0: B1>3; H1: B0 < 3? and then what is the equation to calculate the t-value?

Moreover, in the hypothesis, we test the slope (b1) for simple linear regression (y=b0+b1x) as we want to know their linear relationship. However, the intercept (b0) will also be tested by hypothesis, that is H0: B0=0; H1: B0 not = 0. Although we know the intercept is the predicted y-value when the x-value is 0, what is the purpose for testing intercept by hypothesis? what is the meaning for testing the hypothesis of intercept (B0)?

Thanks.