Explanation for Question 26 From the Math (Calc) Section on the 2019 October Sat
In question 26, we're told that the function F is linear F 2 of two is 17. So really that means that we have a point at 3 two comma 17 and F of eight is 19, 4 which means that we have a 0.8 comma 19. 5 And we know the F of X is in the form, MX plus B 6 where M and B are constants. What is the value of B? 7 And we can remember that in this form, Y intercept form B is our 8 Y intercept. And so the way to find that is first to 9 find the slope, plug the slope into this function. 10 And then from there solve for B, and we can find the slope using 11 these points that they gave us were all called this 0.1. 12 And this 0.2 and the equation for slope M 13 is equal to Y two minus Y one over X two minus X one. 14 So now I can plug in, right? The Y value on 0.2 is 19. 15 So that's why two and the Y value on 0.1 is 17. 16 So that's 17. And then same with the X values. 17 It'll be eight minus two. Now 19 minus 17 is two and 18 eight minus two is six. And I can simplify that by dividing my numerator 19 and my denominator by two. And I get a slope of one third, 20 right? So now all I need to do is plug that into this equation. 21 We have F of X is equal to one third of X plus B. 22 And so now you might be wondering, well, what do I do? I now 23 have three variables. You can take either one of these points to plug in 24 your F of X and your X. That way your only variable is B. 25 So we'll start with this first one F of two is 17. 26 So that means that I have 17 is equal to one third times t...