Explanation for Question 35 From the Math (Calc) Section on the 2018 May Sat
Question 35 says lines T and w are parallel in the X Y plane. 2 The equation of line T is four X plus seven, 3 Y equals 14 and line w passes through negative three eight. 4 What is the value of the Y intercept of line w so to solve 5 this problem, we're going to need to use the Y equals MX plus B 6 formula, which is a formula for a linear equation that tells you what the 7 slope of that line is and what the Y intercept is. 8 So I'm going to take this equation for X plus seven Y and I'm 9 going to put that into Y equals MX plus B four. 10 So I'm going to isolate the Y. So first I'm going to divide both 11 sides by seven to get four over seven X plus Y is equal 12 to two, and then I'm going to subtract negative four over 13 seven X from both sides. 14 So now I know that line T has a slope of negative four over 15 seven at a Y intercept of two, 16 but we're trying to find the Y intercept of line. 17 W however we know that line w is parallel to line T 18 and parallel lines have the same slope, 19 which means that we know that the equation for line w is 20 Y equals negative four, over seven X plus B, 21 and B is the y-intercept that we're solving for. 22 We're also given a coordinate on this line that we can plug in for 23 Y and X to solve for B. So I'm going to do that. 24 I'm going to plug eight in for X, and I'm going to plug negative 25 three in our, sorry, I'm going to plug eight in for Y and negative 26 three in for X, and now I can use this 27 to solve for B. So this becomes eight is equal to 12, 28 over seven plus B. I can subtract 12 over seven from both sides 29 to get eight minus 12, over seven plus B, 30 or is, is equal to B. 31 And then I'm going to change eight into a fraction. 32 So I can do the subtraction by multiplying the top and bottom by seven 33 to get 56, over seven minus 12 or seven is equal to B. 34 And that's just equal to 44 over seven, 35 which is our final answer.