Explanation for Question 19 From the Math (No Calc) Section on the 2018 April Sat
Question 19 says the table above shows two pairs of values for the linear 2 function. AF the function can be written in the form. 3 F of X is equal to X plus B, 4 where and B are Constance. What is the value of a plus B? 5 So at once it's defined an equation for this line in the Y equals 6 MX plus B a F a form. 7 And then it wants us to find what a plus B is. 8 Well, we know that in Y equals MX plus B form M, 9 which is represented here by a, is the slope and B is the 10 Y intercept. So to start, 11 let's try to find a by using the points in this table and the 12 slope formula, which I've written out right here. 13 So Y two is 17. 14 So 17 minus Y one, 15 which is 12 over X, 16 two 12 minus eight, 17 which is X. 18 One is equal to the slope. 19 And so that's five over four. 20 So we know that our slope is five over four, 21 and that's the N value here also represented by now 22 to find the B value. All we have to do is plug in a 23 coordinate that we're given from the table and sell for B. 24 So let's just plug in eight, 12. So 12 is equal to 25 five, over four times eight plus 26 B. Um, 27 so five over four times eight is equal to 40, 28 over four or 10. So this can be rewritten as 12 equals 10 plus 29 B. And if I subtract 10 from both sides, 30 I get two is equal to B. 31 So I know that B is equal to two and that a is equal 32 to five fourths. So now it's asking what is the value of 33 a plus B so five over four plus 34 two, and that's just equal to three and 35 one fourth. And so the correct answer is three and one 36 fourth, or that could also be written as 13 over for.