Limit is H goes to zero of the quantity 4 + sqrt 3 minus the quantity X + H minus the quantity 4 + sqrt 3 - X all over H So the limit is H goes to 0 of 4 + sqrt 3 - X - H - 4 - sqrt 3 - X. If we cancel our force the +4 negative four, we see that we then need to multiply by the conjugate. So sqrt 3 - X - H + sqrt 3 - X We do it to the top, we have to do it to the bottom. When we foil, the first terms multiply together. So the square roots cancel, the outer terms and inner terms are going to cancel, and the last terms multiply together. So the square roots cancel. Remember, it's minus that whole quantity. Now when we look at that term, we can see the three and the -3 is going to cancel the negative X and then minus a negative X is going to cancel. We have negative H / H which is going to turn into -1 so -1 over square root 3 - X -, H + sqrt 3 - X. Now this is still the limit as H goes to 0. So if we stick in H is zero, we get -1 divided by the square root 3 -, X + sqrt 3 - X or -1 / 2 sqrt 3 - X so the slope at -6 seven. Literally we just stick a -6 when we see our X for the derivative. So M equal -1 / 2 square roots 3 - -6 3 - -6 ^2 of 9 ^2 of nine is 3. So the slope turns into -1 six. So y - 7 equal negative one 6 * X + 6 by using point slope form. If we solved point slope form, we distribute the negative 1/6 and we'd add the seven, so we'd get Y equal -1 six X + 6.