Explanation for Question 28 From the Math (Calc) Section on the 2020 October Sat
So here I'm tall, I'm told about two lines lines, 2 Q and lines are, and they're perpendicular to each other. 3 That means that they intersected a 90 degree angle. 4 So they have a perfect cross and they intersected the origin. 5 So both of the points are going to go through this line here at 6 zero zero. And they tell me that line R which I have here in 7 purple passes through the 0.1 comma, 8 K, which I've also drawn on here. 9 And then we want to know the equation for line queue. 10 So first thing we can see is that if it passes through the origin, 11 that means that my Y intercept is zero. 12 So in order to find the equation, I don't have to know anything about 13 the Y intercept, right? It's zero for all of them. 14 So what that means is that if I can find the slope of line 15 queue, then I can find the equation for line queue because the equation is 16 just the slope and nothing else. 17 So now, if I look at line R I see that my Y value 18 for the one point is K. It might feel a little weird that we 19 don't know a number, but we must not need to. 20 So we can just roll with it, put a K wherever we want on 21 the Y axis, and then see where it takes us. 22 And then we know we went over one to get to K. 23 And so since I started at zero zero, my rise is K and 24 my run is one. So my slope of our is 25 K over one. Now this is where the idea that the lines are perpendicular 26 comes into play because lines that are perpendicular have opposite reciprocal 27 slopes. So if the slope of R is K over one 28 first thing I need to do to find the slope of queue is flip 29 it. So that it's one over K that's the reciprocal part. 30 And then the opposite part is that I put a negative sign on it. 31 So the slope of line Q is negative one over K and the only 32 equation that shows that is B. 33 So I correct answer is B.