Explanation for Question 19 From the Math (No Calc) Section on the 2020 October Sat
So question number 19 tells us that we have a system of two linear 2 equations that have no solutions. 3 Of course, we've only graphed one line because we're about to find the other 4 line that makes that system. But talking about no solutions, 5 whenever we're talking about lines, if lines are parallel, 6 then they have no solutions. 7 If lines are perpendicular, you might see this symbol here representing perpendicular. 8 Then they have one solution. And if you have two lines that are the 9 same, then they have infinite solutions. 10 And here we're talking about no solutions. So we want lines that are parallel. 11 And if lines are parallel, then that means that they have the same slope, 12 same slope. So the first thing, most useful thing we can do is figure 13 out what is the slope of the line that we've been given. 14 And we can get that by doing rise over run. 15 So here they've already shown us which two points we can use. 16 If I go up, I go up five. So plus five. 17 And then if I run, I run to the right four. 18 So that's the plus four. So my slope here is five over four. 19 So now I just have to figure out what is a, 20 is a, my slope, or is my a something else. 21 If I write this equation, it's pretty similar to slope intercept form, 22 but it's not exactly the same. So it might be a good idea to 23 put it into the form that you're most familiar with. And that would mean 24 getting this apex to the other side, 25 by subtracting it, and then dividing by negative one 26 so that you can get rid of the negative it's on the Y 27 minus one. And so we see that if we write this equation, 28 slope intercept form, we get Y is equal to eight X minus one that 29 AEs in front of the X, right? So that means that a is my 30 slope. And I need my slope to be the same as the line that's 31 already drawn. So my EI has to be five over four.