Explanation for Question 15 From the Math (No Calc) Section on the 2019 March Sat
Question 15 says in the equation above a and B are constants 2 at a is greater than zero, but less than B, 3 which of the following could represent the graph of the equation in the X, 4 Y plane. So the first step here is to take this original equation up 5 here and to put this into Y equals MX plus B form, 6 because that will tell me what the slope is, the slope and the 7 Y intercept. So let's start by doing that. 8 So we have a X plus B Y is equal to B. 9 I'm going to subtract a X from both sides. 10 That's going to give me negative X plus B is equal to B Y. 11 And then I'm going to divide both sides by B. That gives me negative 12 a over B, X plus B over B, 13 which is just one is equal to Y. 14 Now I know that one is the Y intercept, 15 and I know that the slope is a fraction because a is less than 16 B and that it's negative. 17 So with that information, let's start by finding all the graphs that don't have 18 a y-intercept of one a does. 19 So that could be the answer B doesn't. 20 So we're going to eliminate it. C does, 21 and D does. Now we're going to find all the lines that have a 22 positive slope, because those are not correct as a negative slope C 23 as a negative slope, and D has a negative slope. 24 So those are all still in the running. 25 And then finally, we're going to see which line has a fractional slope. 26 And that line is going to be the correct answer. 27 The slope of a is just one, the rise of runs one. 28 So a is incorrect. The slope of a C 29 is negative one half because it goes down one and over two. 30 So C is the correct answer. And we know this because D has a 31 slope of negative two. That's not a fraction, 32 so it must be C.