Explanation for Question 27 From the Math (Calc) Section on the 2019 April Sat
And 27, we are given the line M which is perpendicular to the line 2 L not shown. And we want to know the equation of line out so 3 we can find the slope of M and then use that slope to 4 find the perpendicular slope, which will be the slope of line L. 5 And using that slope, we can find the equation. 6 So first let's find the slope of them. We look at M I will 7 choose this point here, 8 and this point here, and now we can do rise over run. 9 So it rises 1, 2, 3, 10 and runs 1, 2, 3, 4, 5. 11 So the slope of line M is three over five. 12 So now, since we are looking for a line perpendicular, 13 that means that we have to take the opposite reciprocal of the slope of 14 line M. So if we take the reciprocal, 15 that is five over three, and then changing the sign, 16 the slope will be negative five over three. 17 Now we can plug that into slope intercept form, 18 Y equals MX plus B using our new slope for M Y 19 equals negative five, over three X plus B. 20 Since we don't know the Y intercept of line L it can be any 21 Y intercept and it'll still be perpendicular at some point. 22 So I'm just going to leave out the Y intercept, 23 because the main thing we are looking for here is the coefficients of Y 24 and X. So we need to rewrite it 25 so that it is in standard form. 26 So I'm going to multiply both sides by three, 27 and that gives me three Y equals negative five X. 28 So now, if we add over the five X, 29 that is five X plus three Y plus some number 30 here, I'll just leave it C for a constant, 31 and that is equal to zero. 32 So now, if we look at our answer choices and we need to find 33 an answer that has a five as a coefficient for the X and a 34 positive three as the coefficient for the Y. 35 So that is a five X plus three Y plus three 36 equals zero.