[Video] Q8: Line l in the xy-plane contains points from each of quadrants ii, iii, and iv, but no points from quadrant i. which of the following must be true?

Explanation for Question 8 From the Math (Calc) Section on the Official Sat Practice Test 4

So now we're looking at question number eight, 2 which is telling us about a line, 3 right? That's within our coordinate plane. 4 And I'm going to go ahead and label our axes or not our axes, 5 our quadrants. What's your 1, 2, 3, 6 and four. And we're told that quadrant one doesn't get any action, 7 right? There's no line going through there, but rather there is a line through 8 two, three and four. So we could possibly imagine the line 9 looking something like this, right? 10 Once something that goes through two, three, 11 and four as well. And we can see immediately that this line has a 12 negative slope, which could cause us to choose answer choice D our correct answer. 13 Now, the reason that C is wrong, why the slope can't be positive is 14 because positive slopes have an up and right word trajectory, 15 right? So if I'm going up and right, 16 that means eventually I'm going to hit quadrant one at some point, 17 right? 18 Cause lions go on forever and quadrant one is in the upper right-hand direction. 19 But since I never hit quadrant one, I can't possibly have a positive slope 20 in this case. Now, if the slope is zero, 21 it is a horizontal line and horizontal lines can only go through at most 22 two quadrants, right? Quadrants two and three or quadrants one and two. 23 So since I go through three quadrants, that means that I don't have a 24 horizontal line here. And the same thing for an undefined slope, 25 an undefined slope is a vertical line, which can also go through only two 26 quadrants at a time, either two and three or one in four. 27 And since I go through three quadrants, that means I can't have a vertical 28 line again, leaving me with answer choice D.