ID: a7a14e87
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Linear vocabulary is on full display.
Method 1: To avoid spending time rearranging the answer choices to resemble the more familiar y = mx + b form (even if there is nothing inherently wrong with doing so), you can plug in the point (0, 3) directly, knowing that it must lie on line j.
A. (0) + (3) = 3 √
B. (0) + (3) = -3 X
C. (0) - (3) = 3 X
D. (0) - (3) = -3 √
Now, a little knowledge of perpendicular lines is necessary. The slope of line j should have the opposite sign of the slope of line k. We need not worry about the numbers, since the answer choices are set up without them. Looking at the equation for line k, it is clear that the slope will be negative: y = -x. Thus, between answer choices (A) and (D), we only need to look for which slope would be positive. Answer choice (A) would have -x if we separated x and y, while (D) would have x if we did the same. The correct answer must be (D).
More challenging questions of this type might also incorporate the actual slopes of the lines—e.g., 5/8 and -8/5—but in this problem, there is no need to do any more work than you have to.
Method 2: Plug in the equations to Desmos, from the given equation for line k to each answer choice, and look at the graphs. One of them should not only intersect the first line at a 90 degree angle (and have a slope of 1), but it will also contain the point (0, 3).
Method 3: You can quickly assess the answer choices algebraically by thinking of each option as part of a system of equations.
Line k: x + y = 0
Line j: x + y = +/-3
The answer cannot be (A) or (B), since this system would have no solution: it is impossible for the same variables with the same coefficients to sum to different values. You could now substitute (0, 3) into the remaining answer choices to eliminate (C) on the spot. The correct answer must be (D).
Comments
Post a Comment