[Video] Q30: Question 30 from the math (calc) section of 2018 march sat

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.

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