ID: 98d3393a
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: There is little work to do, but watch out for assumptions.
Method 1: The graph of x = 2, which I will show in a moment below, in method 2, is a vertical line at 2. A perpendicular line to x = 2 would be horizontal, and a horizontal line has a slope of 0, so the correct answer is (A). If you are confused about why the slope of a vertical line is undefined, but the slope of a horizontal line is 0, pick any two points on either line to illustrate.
Line A: x = 2 (vertical line)
m = (y2 - y1)/(x2 - x1) --> m = (anything - anything else)/(2 - 2) --> m = anything/0 = undefined
Line B: y = 2 (horizontal line)
m = (2 - 2)/(anything - anything else) --> m = 0/anything other than 0 = 0
Method 2: Plug in x = 2 to Desmos and graph. You could either write an equation for a perpendicular line or deduce that such a line would have to be horizontal, or y = something (with no x).
Method 3: To avoid making a quick and inaccurate assumption, you could look to disprove the answer choices or think of what would have to be true for them to be accurate.
A. 0
Implication: The line is horizontal, since any two points on that line would have a change in y of 0 but a change in x of something other than 0. A horizontal line is perpendicular to a vertical line, so this answer choice is correct.
B. -1/2
Implication: The line goes down 1 unit for every 2 units it moves to the right when graphed. This is a trap answer for the student who misinterprets the line x = 2 as y = 2x instead.
C. -2
Implication: Now the line goes down 2 units for every 1 unit it moves to the right when graphed. This is a trap answer for the student who might remember that the signs of the slopes of perpendicular lines are opposite, but forgets the part about reciprocals (e.g., 2/3 and -3/2, not 2/3 and -2/3).
D. The slope of x = 2 is undefined, but the slope of a horizontal line would be 0, for reasons explained above, in method 1.
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