line N has slope m = 
given a line with slope m then the slope of a line perpendicular to it is
= - 
thus line N has slope - 
=
77 unicorns, because yesterday the ratio was 6:5 and today it is 3:4. If you add the numbers for both ratios together, you get 11 and 7. Finding the LCM of these two gives 77 (because 7 and 11 are both prime).
You find the LCM of the sums because when you find values based on ratios, you divide value by the sum of the ratio.
e.g. I have 100 fruits. The ratio of apples to oranges is 2:3. How many apples are there?
To solve this you'd add 2 and 3 (5), divide 100 by 5 (20), multiply that by 2 (40) because that's the ratio of apples to oranges.
In this case, you do the reverse. So If I have 77 unicorns, then yesterday there were (77/11 = 7, 7*6= 42, 7*5= 35) 42 green unicorns and 35 yellow. The sum of 42 and 35 is 77. If you do this process with the other ratio you'll get similar results as well.
See the attached image for what the synthetic division table would look like. The cell highlighted in yellow is the remainder.
Final Answer: Choice D) 4
