Explanation for Question 24 From the Math (Calc) Section on the 2019 March Sat
Question 24 says in the X, 2 Y plane, one L has a slope of two. 3 If line K is perpendicular to line out, 4 which of the following could be an equation of line kit. 5 So perpendicular lines have opposite reciprocal slopes, 6 and that's, what's going to be important here since line L has a slope 7 of two. That means the slope of line K is going to be negative 8 one half. So we're trying to find the line out of these four equations 9 that has a slope of negative one half. So to find that we're going 10 to put all the lines into Y equals MX plus B form, 11 and we're going to try to find the slope that has an M value 12 or sorry, the equation that has an end value of negative one half. 13 And since I noticed that most of these are in the form of a 14 negative MX plus Y I'm going to rewrite this like this 15 negative MX plus Y equals B. So we're just going to take each equation 16 and we're going to divide it by whatever the coefficient for the Y value 17 is. 18 Okay. So starting with a, 19 if we take a, and we define both sides by negative five, 20 we get a two X plus Y is 21 equal to negative four, and that doesn't have the right slope. 22 So a is incorrect next. 23 If we divide B by negative six, 24 we get negative one half X plus 25 Y is equal to negative 14 over 26 six. And that also has the wrong slope because we moved the M over. 27 It's actually going to need to be one half, so that's wrong. 28 But if we divide both sides here by negative two, 29 we get negative two X plus Y is equal 30 to 17, over two, actually negative 17 over two, 31 again, that doesn't have the right end value. 32 And so finally, if we divide both sides here by 12, 33 we get one half X plus Y is equal to 34 three. And since in this equation, 35 it's actually negative and one half becomes negative one half. 36 And so D is the correct answer because it has the correct end value 37 of negative one half.