Explanation for Question 12 From the Math (Calc) Section on the 2019 March Sat
Question 12 asks, which of the following equations could define C as a function 2 of T. So this is essentially asking us to take this table right here 3 and then to create an equation using those values. 4 So to do this, we're going to need to use the Y equals MX 5 plus B formula, which tells us how to take data points and put that 6 into a linear equation where M is represented, 7 or the slope is represented by M and the Y intercept is represented by 8 B, and we're gonna need to use the slope formula, 9 which I've written down here, and that you can just use, 10 take two points to calculate the slope. So let's start by finding the slope 11 so we know what the end value should be here. So I'm just going 12 to take these first two data points right here. 13 So I'm going to do 11 minus 8.5 over 14 two minus one. 15 And that gives me 2.5 over one or just 16 2.5. So from that we know that the slope is 2.5 and we can 17 eliminate answers B and answer D. 18 Now what we need to do is we need to take our equation. 19 Y equals MX plus B. 20 We need to plug in the value, 21 which is 2.5. So I'll rewrite this as Y is equal to 2.5 X 22 plus B, and to solve for B, 23 we just need to insert any coordinate here. 24 So I'm going to use the first 1, 1 8 0.5. 25 So Y is equal to 8.5 and that's equal to 2.5 26 times one plus B. 27 So what I'm going to do is subtract 2.5 from both sides, 28 and that's going to give me six is equal to B. 29 And so I know that the Y intercept is six and the answer 30 is a.