so we know the EQUATion of the line, now let's work out the inequality of it.
the shaded area is the "true" region or area, and the non-shaded is the "false" region, hmmm let's work our way from the "false" region.
first off, the line is solid, that means the line includes values in the inequality, meaning the shaded part extends to the borderline, so the inequality will be either ⩾ or ⩽, let's work it out from the "false" region, by picking out a point there, hmmm let's use say x = 6 and y = -4, so the point is (6 , -4) and let's plug it in the EQUATion.
well, clearly -4 is less than 1.5, however to make that a false statement, we can say that -4 is more than 15, now, is not true, is "false" and since we're working from the "false" region, that is what we need, "more than", or ⩾
now, bear in mind that we could have started from the "true" region, the shaded one, and pick a point in it like (0 , 0), if you test, that gives us something like 0 [ ] -3, to make that true, we make it 0 ⩾ -3, because that is true, 0 is really greater than -3, and working for the "true" region, that's what we need.