Explanation for Question 30 From the Math (Calc) Section on the 2018 March Sat
Question 30 says in the X, Y plane above blinds, 2 K and L or perpendicular, what does the X coordinate of point P? 3 So first we need to find the slope of this line right here, 4 line L. And we know that that slope is three over four. 5 And we know that because this coordinate, uh, 6 sorry, this point goes through zero zero, and this point goes through four, 7 three. So it goes up three over four then because the two lines are 8 perpendicular. We know that this other line line K has an opposite reciprocal 9 slope. So that means the sub of this line is negative four over 10 three. Now, from that we can use the Y equals MX plus B formula 11 or N represents the slope and B represents the Y intercept to figure out 12 what the answer is. So first I'm just going to plug in negative four 13 for three for M I'm going to keep be the same. 14 Now we can plug in a point that we know is on the line 15 for three to figure out what B is. 16 So three is equal negative four, 17 over three times four plus B, 18 that becomes B is equal to negative 16, 19 over three plus B. And when I add negative 16, 20 over three to both sides, I get 25. 21 Over three is equal to B. 22 Then finally, I can plug that back into my original equation and get Y 23 equals negative four over three X plus 25 over three. 24 And if I want to find what this coordinate is, 25 this P value right here is all I have to do is plug in 26 zero for Y. So if I do that, 27 I get zero is equal to negative four for three X plus 28 25, over three. That gives me if I subtract 25 over three from 29 both sides, negative twenty-five over three is equal to negative four, 30 over three X. And if I divide both sides by negative four for three, 31 I get 6.25, oops, 32 6.25 is equal to X. 33 And that's our answer here. So the answer is.