Explanation for Question 25 From the Math (Calc) Section on the Official Sat Practice Test 6
Question 25 gives us this table. 2 And then it says some values of the linear function F are shown in 3 the table above what is the value of F of three. 4 So we know that it's a linear function and we have enough information from 5 this table to get us a simple linear equation. 6 So Y equals MX plus B with BB in the Y intercept and end 7 being the slope. So to find slope, 8 we need two points, which we have, 9 and we're going to do Y two minus Y one over X, 10 two minus X one. And let's pick the points zero negative two 11 and two four. So Y two is four minus 12 negative two, and then X two 13 is two minus zero. 14 So four minus negative two is just going to be four plus two, 15 which is six. Over two is equal to three. 16 So now we know that, um, is equal to three and B it's very 17 easy to find. 18 Um, all we have to do for this one is we need to 19 see where the Y intercept is. 20 And that's one of the points given to us because they say that when 21 X is equal to zero, Y is equal to negative two or F of 22 X is equal to negative two. So if you picture that in a graph, 23 when X is equal to zero, Y is negative to ensure enough, 24 that's a Y intercept. Now, 25 knowing that the slope is equal to three, our graph is going to look 26 something like that. So we're left with the expression, 27 Y equals three X minus two. 28 So now we can just plug in X is equal to three. 29 Y is equal to three times three minus two. 30 So three times three is nine minus two is seven. 31 So Y is equal to seven, which is the same thing as F of 32 three is equal to seven. 33 So we can circle B as our answer choice.