ID: 78391fcc
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Knowing key terms helps, but the table and answer choices point to the correct line of reasoning, just in case.
Method 1: The x-intercept of a graph is where y = 0, so the question is really asking, "What is the value of x when y, or f(x), is 0?" Looking at the f(x) row, we can see that each shift to the right drops the value by 3: 21 --> 18, 18 --> 15, 15 --> 12. Likewise, we can glean from the x row that each shift to the right increases the value by 1: -11 --> -10, -10 --> -9, -9 --> -8. We can calculate a slope, but we can just as easily work with the same concept in our head (or on paper) by applying the same logic that we have already observed in the table:
- to get from 12 to 0 in the f(x) row would take 4 shifts to the right (remember, each shift is -3)
- if each shift to the right in the x row increases the value by 1, then 4 shifts to the right would be (-8 + 4), or -4
The correct answer must be (B), (-4, 0).
Method 2: You can use Desmos to solve for the slope and then create a slider for b in y = mx + b. As long as you can locate any other point from the table, you must have the correct value, since you are dealing with a line (and all the other points would have to lie on the line as well). How about (-10, 18)?
Method 3: The textbook way to solve the problem is to calculate the slope of the line, solve for b in y = mx + b, then substitute 0 for y (or f(x)) and find the corresponding value of x. However, that seems like a lot of extra work. You really only need to consider answer choices (A) or (B). Answer choice (C) cannot be correct: the point (-9, 15) is given in the table, so (-9, 0) would not be a point on the line. Answer choice (D) also makes no sense, since -12 in the top row would lead to a value greater than 21, without even getting precise. You can compare slopes between (A), (B), and the known slope calculated from any two points in the table. How about we start from the left with (-11, 21) and (-10, 18)?
m = ((18) - (21))/((-10) - (-11))
m = -3/1 or -3
If (A) is correct, the slope must be -3/1. Test the point (-3, 0) alongside, say, (-8, 12):
m = ((12) - (0))/((-8) - (-3))
m = 12/-5
m ≠ -3
Even without testing (B), it is clear that it must be the correct answer: nothing else works. For the fact-checker out there, use the same point from the table as before:
m = ((12) - (0))/((-8) - (-4))
m = 12/-4
m = -3
The correct answer is (B).
This method could prove just as fast as either of the above methods, and it takes nothing more than an understanding of how to calculate a slope.
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